ccording to figures published by Forbes magazine in September 2002, his net

Transcription

1 A ccording to figurs publishd by Forbs magazin in Sptmbr 2002, his nt worth was stimatd to b US$43 billion! This is th quivalnt of about A$83.4 billion. It is intrsting to not that Bill Gats s nt worth fll about US$11 billion ovr th last yar. That mans h lost about US$30 million a day. You can t hlp bad luck. In 2001, th richst Australian was Krry Packr, who had a nt worth of US$2.5 billion, which is about on-third of Bill Gats s losss ovr th yar. Thr wr two othr Australian billionairs Frank Lowy and Richard Pratt. On positiv aspct of his walth is that Bill Gats donats many millions of dollars to halth car. As an xampl, h has donatd ovr US$50 million to AIDS/HIV rsarch. hi.com.au 1

2 Worksht R1.1 Worksht R1.2 Worksht R1.3 Worksht R1.4 Worksht R1.5 Worksht R1.6 Worksht R1.7 Worksht R1.8 Prpar for this chaptr by attmpting th following qustions. If you hav difficulty with a qustion, click on th Rplay Worksht icon on your Maths Zon CD or ask your tachr for th Rplay Worksht. 1 Convrt th following fractions to dcimals (a) (b) (c) Convrt th following dcimals to fractions (in simplst form, whr appropriat). (a) 0.79 (b) (c) Evaluat th following, without using a calculator (a) (b) (c) (d) Evaluat th following, without using a calculator. (a) (b) (c) (d) A pic of matrial 8 m long is cut into two pics, on 3 m long and th othr 5 m long. What is th ratio of th smallr pic to th largr? 6 $20 is dividd btwn Anh and Kiao in th ratio 3 : 1. How much dos ach rciv? 7 Find: 1 (a) 5% of 20 m (b) 2 -- % of $60 (c) 115% of $860 8 Find x if: (a) 500 = 20x (b) 35 = 2x (c) 4.2 = 0.6x amount buying on trms chqu commission crdit card dbit card dfrrd paymnt dposit discount EFTPOS gross arnings gross incom gross pay HECS hir purchas incom incom tax instalmnt lay-by loss nt arnings nt pay ovrtim PAYG prsonal loan pic work principal profit rat of intrst rtainr salary simpl intrst suprannuation tak-hom pay tax dduction taxabl incom tax rturn wags 2 Hinmann MATHS ZONE

3 It is usful to bgin this chaptr with a quick rviw of fractions, dcimals, prcntags and ratios. Fractions and dcimals workd xampl 1 Evaluat th following. (a) 2 1 (b) (c) (d) Stps (a) 1. Chang mixd numbrs to impropr fractions. 2. Convrt to a common dnominator. = Prform th subtraction. = or (b) 1. Chang mixd numbrs to impropr fractions. (b) 2. Convrt to a common dnominator. = 3. Prform th addition. = 4. Writ th answr as a mixd numbr. = (c) 1. Chang mixd numbrs to impropr fractions and dcid on th ovrall sign of th product. Solutions (a) = Cancl (if possibl). = Prform th multiplication. = Writ th answr as a mixd numbr. = (c) = = mony CALCULATIONS 3

4 (d) 1. Chang mixd numbrs to impropr fractions. 2. Chang th to a and invrt th fraction aftr th opration symbol Cancl (if possibl). = (d) 4. Prform th multiplication. = 5. Writ th answr as a mixd numbr. = = = Dcimal calculations, at this stag, ar probably bst handld by calculator if you cannot do thm in your had. You will probably find that you can actually answr many dcimal qustions using mntal arithmtic skills. workd xampl 2 Evaluat th following. (a) (b) (c) (d) Stps Solutions (a) Us your calculator to find th answr. (a) = (b) Us your calculator to find th answr. (b) = (c) Us your calculator to find th answr. (c) = (d) Us your calculator to find th answr. (d) = 5.65 Convrting fractions and dcimals Whn w want to convrt a fraction or a mixd numbr to a dcimal, or a dcimal to a fraction or mixd numbr, w should ralis that th whol numbr part will rmain th sam. So w only hav to chang th fraction part or th part aftr th dcimal point. Whn convrting dcimals to fractions, th numbr of zros in th dnominator is qual to th numbr of digits aftr th dcimal point. 4 Hinmann MATHS ZONE

5 workd xampl 3 (a) Writ as a dcimal. (b) Writ as a fraction in simplst form. Stps Solutions (a) Ky in (a) 2 3 = = (b) 1. Writ th dcimal part in fraction form. (b) = Cancl down. (Us your calculator to do 624 = this if ncssary.) Writ th solution = Your calculator can toggl btwn fraction and dcimal mods. Prcntags Prcntags ar anothr way of xprssing fractions, or th portion of chang in quantitis. Pr cnt is drivd from th Latin pr cntum, which mans by th hundrd. workd xampl 4 (a) Find what prcntag 50 is of 80. (b) Find th rsult whn 2100 is incrasd by 22%. (c) What is th rsult whn 2400 is rducd by 45%? Stps (a) 1. Writ th comparison as a fraction tims 100, and attach th % symbol. 2. Us your calculator to find th answr. Entr Solutions 50 (a) % 80 = 62.5% = 1.22 is th dcimal ratio nw : old.. Writ th answr. (b) 1. Find th ovrall prcntag and writ in (b) 100% + 22% = 122% dcimal form. = Multiply th quantity by th dcimal ratio = 2562 (c) 1. Find th rducd prcntag and writ in dcimal form. (c) 100% 45% = 55% = Multiply th quantity by th dcimal ratio = 1320 Tutorial 1 mony CALCULATIONS 5

6 As with many calculator xrciss, ths xampls could hav bn approachd in a varity of ways. Ratios This yar w ar intrstd in looking at incrasing or dcrasing quantitis in a givn ratio, just as w hav bn doing with prcntags. This procss is achivd simply by multiplying th quantity by th ratio xprssd in fraction form. Whthr w ar incrasing or dcrasing a quantity, th ratio is bing xprssd in th ordr nw : old. Th ordr of a ratio is important. In gnral, a : b b : a. a Th ratio a : b can b writtn as -, b giving th sam valu as th dcimal ratio obtaind from th quotint a b. workd xampl 5 (a) Incras $400 in th ratio 6 : 5. (b) Dcras 330 m in th ratio Stps Solutions (a) 1. Exprss th ratio in fraction form. 6 (a) 6:5 = Multiply th quantity by th fraction. 6 $ = $480 5 (b) Multiply th quantity by th fraction. 2 (b) 330 m = 220 m 3 -- xrcis 1.1 Fractions, dcimals, prcntags and ratios Prparation: Prp Zon Q1 to Q7 1 Evaluat th following. (a) 3 1 (b) (c) (d) 2 5 () (f) (g) 2 3 (h) (i) (j) (k) (l) Evaluat th following. (a) (b) (c) (d) () (f) (g) (h) (i) (j) (k) (l) Convrt th following fractions to dcimals. (a) (b) 3 -- (c) (d) () (f) Intractiv hi.com.au 6 Hinmann MATHS ZONE

7 4 Convrt th following dcimals to fractions in thir simplst form. (a) (b) (c) (d) () (f) Choos th corrct answr is closst to: A 1.42 B C 1.42 D 6.26 E Choos th corrct answr is closst to: A B 3 -- C D E 7 Find what prcntag: (a) 30 is of 90 (b) 25 is of 125 (c) 40 is of 120 (d) 20 is of 110 () 15 is of 100 (f) 25 is of 80 (g) 16 is of 45 (h) 21 is of 120 (i) 32 is of 85 8 Find th rsult whn 1500 is incrasd by: (a) 15% (b) 25% (c) 45% (d) 120% 9 Find th rsult whn 2200 is rducd by: (a) 10% (b) 40% (c) 66% (d) 95% 10 (a) Incras $50 in th ratio 7 : 5. (b) Dcras $75 in th ratio 8 :15. (c) Dcras 250 m in th ratio 4 : 5. (d) Incras 513 m in th ratio 10 : () Incras 400 minuts in th ratio (f) Dcras 450 minuts in th ratio Writ thr whol numbrs that whn incrasd in th ratio 7 : 3 giv an answr btwn 100 and Copy and complt th following tabl Writ answrs corrct to two dcimal placs whr ncssary. (a) Common fraction Dcimal fraction Prcntag Ratio (b) 0.45 (c) 72% (d) 2:5 () 0.56 (f) 3:8 13 Th studnt population at Growthtown High School this yar is 840. This rprsnts an incras of 20% ovr last yar. (a) What was th studnt population last yar? (b) If a furthr growth of 15% is prdictd for nxt yar, what will th studnt population b thn? Animation 1 mony CALCULATIONS 7

8 14 Th numbr of schools participating in a particular local maths day this yar compard to last yar has incrasd in th ratio 6 : 5. (a) If fiftn schools participatd last yar, how many ar participating this yar? (b) Exprss th incras as a prcntag. Qustions Elction rsults Th rsults of th school lction for comdy qun wr writtn up in th school nwslttr as follows: Fifty vots ahad of hr closst comptition, Ambr will b our nw comdy qun, obtaining 35% of all vots. Bc cam in scond plac, with Cathrin not far bhind hr obtaining 134 mor vots than Dirdr. Dirdr obtaind 12% of all vots. If ths four girls wr th only candidats, find th numbr of vots ach obtaind. Mayb w could lt x stand for th total numbr of vots. Whn w work w usually xpct to gt paid for th work w hav don. Th paymnt w rciv can b calculatd in a numbr of ways dpnding on th typ of work w ar doing or on th typ of mploymnt contract w hav signd. Pic work largly applis in manufacturing, spcially in th clothing industry. Pic work mans workrs in a factory or at hom ar paid pr itm (or garmnt) producd, rathr than for th numbr of hours workd. 8 Hinmann MATHS ZONE

9 workd xampl 6 Emma is mployd swing drsss. Sh is paid at th rat of $7.50 pr drss and sh can complt 42 drsss ach wk. Calculat hr arnings pr wk. Stp Multiply th numbr of itms producd (42) by th rat ($7.50). Solution Earnings = 42 $7.50 = $315 Wags largly apply to factory work, trads, som offic work, and shop work. Wags ar basd on an hourly (or standard) rat of pay. Thr is a maximum numbr of hours that an mploy may work within spcifid hours according to th rlvant industrial award. Any xtra work may b paid as ovrtim at a highr hourly rat. workd xampl 7 Sim is mployd at a photographic studio. H rcivs $12.30 pr hour for a standard 35-hour Monday to Friday wk, but on Saturday h is paid tim-and-a-half (i tims th standard hourly rat) for th first 3 hours and doubl tim (twic th standard rat) thraftr. On particular wk, Sim workd 4.5 hours on Saturday in addition to th standard hours. How much mony did h arn? Stps 1. Calculat th numbr of hours workd at ach of th rats. 2. Multiply ach numbr of hours by th appropriat hourly rat. 3. Add up th individual amounts to find th total wag. Solution Standard hours: 35 Tim-and-a-half: 3 hours (first 3 hours on Saturday) Doubl tim: 1.5 hours (th rst of th tim on Saturday) Standard hours: 35 $12.30 = $ Tim-and-a-half: 3 $ = $ Doubl tim: 1.5 $ = $ Total = $ mony CALCULATIONS 9

10 Commission is usually paid to salspopl, such as ral stat agnts, car sllrs and sals rprsntativs. Dpnding on th typ of slling, salspopl usually hav to kp som offic hours, so a rtainr or flat amount pr wk is also paid. Th commission is an xtra paymnt of a prcntag of th valu of th sals mad. To calculat th amount of commission (C) to b paid you nd to multiply th rat of commission (R) by th slling pric (SP) of th goods. W xprss this as a formula: Commission = rat slling pric C = R SP workd xampl 8 Lina works as a ral stat agnt. Sh rcivs a rtainr of $130 pr wk plus commission on sals. Th rat of commission is variabl, with a 0.5% commission on th first $ and 0.25% thraftr. (a) How much is sh paid if sh slls a flat for $ ? (b) How much is sh paid if sh slls a hous for $ ? Stps Solutions (a) 1. Writ th formula conncting C, (a) C = R SP SP, R. 2. Convrt R into a dcimal. R = 0.5% = Substitut th known information into th formula and calculat th commission. C = $ = $ Add th commission to th rtainr. Total paid = $( ) = $780 (b) 1. Writ th givn valus for th first part. 2. Us th formula to calculat th commission. 3. Writ th givn valus for th rmaindr. 4. Us th formula to calculat th commission. 5. Add both parts of th commission to th rtainr. (b) First $ : R = 0.5% = C = $ C = R SP = $ = $750 Rmaindr: R = 0.25% = SP = $( ) = $ C = $ = $175 Total paid = $( ) = $ Hinmann MATHS ZONE

11 workd xampl 9 An ncyclopdia salsprson rcivs a commission of $450 on th sal of a $2680 st of ncyclopdias. Calculat th rat of commission. Stp Find th commission as a prcntag of th slling pric. (Round to two dcimal placs.) Solution $450 Rat = % $ % Salary is normally paid to mmbrs of staff in profssional jobs. At lowr lvls of salary, mploys may b paid for ovrtim, or rciv som tim off instad. At highr lvls, th rmunration is oftn givn for th job don, rgardlss of th numbr of hours workd. Earnings Pic work: Paymnt pr itm producd. Wags: Hourly rat of pay. Extra work may b paid as ovrtim at pnalty rats (tim-and-a-half, doubl tim). Commission: Prcntag of th valu of sals mad (additional to a possibl rtainr or flat f). Commission = rat slling pric C = R SP Salary: Wkly, monthly or annual rat of pay. Ovrtim may b paid, or tim off givn instad. xrcis 1.2 Earnings Prparation: Exrcis A smitrailr drivr is paid $12.75 pr tonn of timbr dlivrd to a wood-chipping mill. If h dlivrs 120 tonns to th mill, how much will h b paid? 1 mony CALCULATIONS 11

12 2 A drivr of an or carrir is paid at th rat of $25.70 pr load. In a day a drivr dlivrs svn loads. How much is sh paid? 3 A tam of factory workrs is paid $4.40 pr tyr producd. In a full shift, a tam of fiv producs 102 tyrs. How much dos ach prson arn that day? 4 Choos th corrct answr. A casual workr is paid 15 cnts to produc rostts in football colours. If h producs 1500 in a two-wk priod, h will rciv: A 1500 $15 B 1500 $0.15 C 1500 $15 2 D 1500 $ E 1500 $ Choos th corrct answr. A casual workr arns $8.75 pr hour stacking shlvs in a suprmarkt. If sh works 18.5 hours in 5 days sh will b paid: A 18.5 $8.75 B 18.5 $ C 18.5 $ D $ E 18.5 $ A turnstil oprator at th football is paid $7.75 pr hour. How much will h arn if h works: (a) 4 hours? (b) 5.5 hours? (c) 7.5 hours? (d) 6 hours? 7 Choos th corrct answr. If a factory workr, paid at th rat of $7.80 pr hour, works 7 hours at standard rat plus 3 hours at tim-and-a-half and 1 hour at doubl tim, th wags for that day will b: A $( ) B $( ) C $( ) D $( ) E $( ) 12 Hinmann MATHS ZONE

13 8 In a small T-shirt-printing factory th following tim shts summaris th hours workd by four mploys. Calculat thir total arnings for th wk if th standard rat is $11.40 pr hour. Nam Standard hours Tim-and-a-half Doubl tim Adam Britta Con Dng An lctrical rpairr is paid $12.70 pr hour for a standard 35-hour wk, plus tim-and-a-half for th first 3 hours on Saturday and doubl tim for any hours aftr that. How much will h rciv if h works a standard wk, and thn 4 hours of ovrtim on Saturday? 10 A printr is paid $10.45 pr hour for a standard 35-hour wk plus tim-and-a-half for th first 2 hours of ovrtim on any day and doubl tim for any hours aftr that. If sh works a standard wk and thn works 1.5 hours xtra on Thursday and 4 hours xtra on Friday, how much pay will sh rciv? 11 Choos th corrct answr. A salsprson is paid $130 rtainr pr wk plus 2.5% of sals. If $ worth of goods is sold during on wk, his arnings will b: A $( ) B $( ) C $( ) D $( ) E $( ) 12 Abigail is paid a rtainr of $120 pr wk plus 15% of th valu of sals. Calculat th incom sh arnd in a wk in which sh sold goods to th following valus. (a) $4340 (b) $2901 (c) $1409 (d) $ Choos th corrct answr. If commission of $58 is arnd on sals of $1700, th prcntag paid is: A % B % C % D % E % Calculat th prcntag commission paid in ach of th following cass. (a) SP = $540, C = $45 (b) SP = $8700, C = $580 (c) SP = $2500, C = $ Fran is paid $612 commission on sals of computr softwar. Writ thr possibl pairs of valus for prcntag commission and slling pric, givn that commission rangs btwn 10% and 20% for ths typs of sals. 1 mony CALCULATIONS 13

14 16 A computr salsprson rcivs 4.5% of sals as wll as a rtainr of $110 pr wk. In a wk whn h slls $ worth of quipmnt, how much mony will h rciv? 17 A car salsprson is paid a rtainr of $180 pr wk plus a commission of 1.3% on sals. In a wk in which sh slls a Commodor for $ and a Barina for $13 000, how much will sh b paid? 18 A ral stat agnt is paid commission on th sal of houss at th following rat: 2% on th first $ % on th nxt $ % on th rst How much would th sllr hav to pay in commission if a hous was sold for: (a) $85 000? (b) $ ? (c) $ ? (d) $ ? () $ ? (f) $ ? 19 Givn that thr ar about 52 wks or 26 fortnights in a yar and xactly 12 months in a yar, copy and complt th following tabl to show arnings for ach priod. Writ answrs to th narst dollar. To convrt from wkly to monthly, first convrt to yarly. (a) $450 Wkly Fortnightly Monthly Yarly (b) $670 (c) $ (d) $1450 () $3620 (f) $ Anothr diffrnc btwn a wag and salary is that som typs of paymnts ar additional to wag arnings, but ar alrady incorporatd into a salary. (a) Hilda gts paid a wag that amounts to $450 wkly. Hr lav loading, addd onto hr pay for holidays, is 17.5% of this amount. (i) Calculat hr lav loading pr wk. (ii) What pay will sh rciv during a two-wk holiday priod? (This includs hr normal incom plus lav loading.) 14 Hinmann MATHS ZONE

15 (b) Barry s incom amounts to $1250 fortnightly. If h rcivs lav loading of 17.5%, what pay will h rciv for a four-wk holiday priod? 21 Christi has startd up a small company and has dcidd to rward hr staff with a bonus by distributing 5% of any profits vnly btwn thm. In th first yar th company maks a profit of $ Givn that Christi has 20 mploys, how much will ach rciv as a bonus? Bfor tax, a prson s wag or salary is oftn rfrrd to as gross arnings or gross pay. Th amount rmaining aftr tax and othr amounts such as union fs hav bn takn out is rfrrd to as nt arnings, nt pay or tak-hom pay. Th Fdral Govrnmnt rquirs a proportion of mploy arnings to b withhld by mployrs as incom tax.undr th PAYG (Pay As You Go) systm in Australia, mployrs withhold tax on a rgular basis and forward it to th govrnmnt. Suprannuation is an amount an mployr pays on bhalf of mploys into a fund that mploys can accss at rtirmnt, or arlir in xtrm situations. Th amount is 9% of an mploy s gross arnings, but is not dductd from thir pay; it is an additional amount. Many mploys can also contribut prsonally to a suprannuation fund by dductions from thir pay. Employs may also arrang for othr amounts (.g. union fs) to b dductd from thir pay. In gnral: Nt arnings = gross arnings tax agrd dductions workd xampl 10 Calculat th nt arnings if gross arnings ar $1250, tax is $ and a prsonal suprannuation dduction of $42.50 is mad. Stp Subtract tax and prsonal suprannuation from gross pay. Solution Nt arnings = $1250 $ $42.50 = $ mony CALCULATIONS 15

16 workd xampl 11 Kat s gross pay ach fortnight is $980. (a) Kat pays 19% of hr gross pay in tax. What is hr nt fortnightly pay? (b) What amount must hr mployr contribut to Kat s suprannuation fund ach fortnight? Stps Solutions (a) 1. Calculat th amount of tax withhld. (a) 19% of $980 = 0.19 $980 = $ Subtract this amount from gross fortnightly pay to find nt fortnightly pay. (b) Calculat 9% of gross pay. Nt fortnightly pay = $980 $ = $ (b) Fortnightly suprannuation = 9% of $980 = 0.09 $980 = $88.20 Incom includs all mony arnd and mony rcivd from businss activitis and invstmnts. At th nd of th financial yar, popl who hav rcivd incom in Australia complt a tax rturn. This is usd to assss whthr th total amount of tax paid ovr th yar is corrct, considring all factors, such as gross incom, work-rlatd xpnss and othr allowabl dductions. Dpnding on th tax rturn, an individual may rciv a tax rfund or may hav to pay mor tax. Gross incom is your total incom, bfor tax is paid or any dductions ar mad. Taxabl incom is th amount of your incom that th govrnmnt blivs you should pay tax on. If you hav mad paymnts that ar work-rlatd or hav givn mony to rcognisd charitis, th law stats that you do not hav to pay tax on ths amounts. So bfor th total amount of tax you should pay is calculatd, som allowabl tax dductions ar mad from gross incom. Taxabl incom = gross incom allowabl tax dductions Th tabl blow (July 2003 figurs) shows how annual incom tax is calculatd. Taxabl incom Tax on this incom $1 $6000 Nil $6001 $ cnts for ach $1 ovr $6000 $ $ $ cnts for ach $1 ovr $ $ $ $ cnts for ach $1 ovr $ $ and abov $ cnts for ach $1 ovr $ Hinmann MATHS ZONE

17 workd xampl 12 Carri s annual gross salary is $ During th yar sh had work-rlatd xpnss totalling $1200, paid union fs of $255 and donatd $650 to rcognisd charitis. (a) Calculat Carri s taxabl incom. (b) Calculat how much tax Carri should hav paid using th tabl on pag 16. Stps (a) Subtract allowabl dductions from gross incom. (b) 1. Locat th taxabl incom in th tabl and writ th statmnt about tax payabl. 2. Calculat th numbr of dollars abov th lowr limit. 3. Calculat tax payabl by using th statmnt from th tabl. Solutions (a) Taxabl incom = $ ($ $255 + $650) = $ $2105 = $ (b) Tax payabl is $ cnts for ach $1 ovr $ $ $ = $895 Tax payabl = $( ) = $ xrcis 1.3 Incom tax Prparation: Exrcis Calculat th nt arnings whn: (a) gross arnings = $875, tax = $149.40, prsonal suprannuation = $42.30 (b) gross arnings = $529, tax = $98.70, prsonal suprannuation = $26.35 (c) gross arnings = $1263, tax = $278.50, union fs = $5.50 (d) gross arnings = $4670, tax = $ , othr dductions = $ Jard s gross wkly pay is $ If 22% of this is withhld as PAYG tax, what is Jard s nt wkly pay? 3 Suzann s gross monthly pay is $ Sh pays 5.7% of this into hr suprannuation fund and 25.8% is withhld in tax. Suzann also pays monthly union fs of $ What is Suzann s nt monthly pay? 4 Givn that an mployr must pay an amount qual to 9% of an mploy s salary into a suprannuation fund, how much supr will b paid for ach of th following annual salaris? (a) $ (b) $ (c) $ (d) $ () $ (f) $ mony CALCULATIONS 17

18 In th following qustions, us th tabl on pag 16 to calculat tax payabl. 5 How much incom tax should b paid on ach of ths taxabl incoms? (a) $5200 (b) $7500 (c) $ (d) $ () $ (f) $ (g) $ (h) $ (i) $ (j) $ (k) $ (l) $ Choos th corrct answr. Th tax payabl on $ is closst to: A $7380 B $6274 C $4274 D $9894 E $ Choos th corrct answr. Th tax payabl on $ is closst to: A $ B $ C $ D $ E $ Rosanna rcivs an annual gross incom of $ (a) What is hr taxabl incom if sh donats $360 a yar to Amnsty Intrnational and has work xpnss totalling $575? (b) Calculat how much incom tax Rosanna should pay annually. 9 Jan arns an annual gross salary of $ and maks rgular contributions to rcognisd charitis that total at last $450 pr yar. (a) Writ thr possibl taxabl incom amounts for Jan. (b) Calculat th tax payabl on on of ths amounts. 10 Karl s fortnightly gross pay is $1256. Karl has annual union fs, which h has paid up-front, of $125. H sponsors a child for $420 pr yar and has annual work-rlatd xpnss of $320. H has no othr incom. (a) What is Karl s annual gross incom? (b) What is Karl s taxabl incom? (c) How much pr yar should Karl pay in tax? Thr ar 26 fortnights in a yar. 11 At th bginning of th financial yar, Justin startd in a nw position with an annual gross salary of $ (a) How much should Justin pay pr yar in tax? (b) How much is Justin s wkly gross pay (to th narst dollar)? (c) How much pr wk of Justin s salary is withhld as PAYG tax? Thr ar 52 wks in a yar. Justin lavs hr job aftr 34 wks in th position, and travls around Australia without working for th rst of th financial yar. Bfor laving, Justin arnd $ and paid $8031 in PAYG tax. (d) Calculat how much tax Justin should pay on th amount sh arnd in th financial yar. () How much tax should Justin b rfundd? Round your answr to th narst dollar. 18 Hinmann MATHS ZONE

19 12 Hln has dcidd to contribut prsonally to hr suprannuation fund so that sh may hav a mor comfortabl rtirmnt. Hr annual salary is $ (a) What amount must hr mployr contribut to Hln s suprannuation fund, if th rquird contribution is 9% of th gross salary? (b) Hln dcids to contribut 5% of hr salary to hr suprannuation fund. How much will sh contribut ach yar? (c) Hln has work-rlatd xpnss this yar totalling $1523. Find Hln s taxabl incom. (d) How much tax should Hln pay this yar? Homwork 1.1 Any prson or organisation borrowing mony usually pays for th us of that mony in th form of intrst. Whnvr th intrst is calculatd on th amount borrowd and not addd onto th original sum, it is calld simpl intrst (I). Th amount of intrst du dpnds on th amount borrowd, calld th principal (P), th rat of intrst (R) in pr cnt pr yar (pr annum; p.a.), convrtd to a dcimal, and th tim (T) in yars. Thus th formula for calculating simpl intrst is I = PRT workd xampl 13 Calculat th simpl intrst paid on a loan of $5000 at 16.4% intrst ovr 4 yars. Stps Solution 1. Idntify th quantitis givn. P = $5000, R = 16.4% = 0.164, T = 4 2. Writ th simpl intrst formula. I = PRT 3. Substitut and calculat. = $ = $3280 It is important to ralis that th simpl intrst formula givs you th amount of intrst paid or du. To find th total amount (A) of mony paid or du you nd to add th principal to th simpl intrst. A = P + I If th loan is rpaid in instalmnts,th amount of ach of ths qual rpaymnts can b calculatd: A Instalmnt = --- whr n is th numbr of instalmnts. n 1 mony CALCULATIONS 19

20 workd xampl 14 Barbara borrows $2400 to st up a businss. Sh is chargd intrst at 18.5% p.a. and maks quartrly paymnts ovr 5 yars and 3 months. (a) What is th total amount of mony to b rpaid? (b) How much must sh pay quartrly? Stps Solutions (a) 1. Idntify th quantitis givn. (a) P = $2400 R = 18.5% = T = = Writ th simpl intrst formula. I = PRT 3. Substitut and calculat. = $ = $ Writ th formula for total A = P + I amount payabl. 5. Substitut and calculat. = $ $2331 = $4731 (b) 1. Calculat th numbr of (b) n = instalmnts. = 21 A 2. Find th amount of ach Instalmnt = --- n instalmnt. $4731 = $ pr quartr Th tim priod will not always b a whol numbr of yars. In cass lik this you simply xprss th tim priod in fraction form and substitut as normal. Most banks us simpl intrst to calculat th amount of intrst payabl on accounts. Thr ar two major mthods usd: intrst calculatd daily, or intrst calculatd monthly basd on th minimum monthly balanc in th account. On of th difficultis associatd with ths calculations is working out th numbr of days that ach balanc applis for. Th chang taks plac on th day th withdrawal or dposit is mad. For xampl, in Workd Exampl 15 blow, th balanc of $ applis to Sptmbr 1, 2, 3, 4 and 5 (i.. 5 days). Mak sur th numbr of days you us in your calculations is th total numbr of days in that month. workd xampl 15 Craig s passbook for Sptmbr looks lik this: If th account pays 6% intrst, calculat th intrst accrud in Sptmbr if intrst is calculatd: (a) daily to six dcimal placs (b) on th minimum monthly balanc. Dat Transaction Amount Balanc Sp 1 Sp 6 Sp 19 Balanc Dposit Withdrawal $180 $400 $ $ $ Hinmann MATHS ZONE

21 Stps Solutions (a) 1. Idntify P, th balancs. (a) P = $490.15, $670.15, $ Idntify th rat R. R = 6% = Idntify th tim T in yars for ach balanc. 4. Writ th simpl intrst formula. 5. Substitut into th formula th rspctiv valus of P, R and T and calculat corrct to six dcimal placs. 6. Calculat th total intrst by adding th individual amounts. 7. Round off to two dcimal placs (i.. th narst cnt). T = I = PRT 5 Sp 1 5: I = $ $ Sp 6 18: I = $ $ Sp 19 30: I = $ $ Total: I = $ $ $ = $ $2.37 (b) 1. Idntify th smallst balanc. (b) $490.15, $670.15, $ So P = $ Idntify th rat R. R = 6% = Idntify th tim T in yars. 1 T = Writ th simpl intrst formula , 365 I = PRT , Substitut and calculat. = $ $ It is much asir to calculat th intrst basd on minimum monthly balanc than on daily balanc, although computrs mak this asir. For simpl intrst calculations: I = PRT whr I = simpl intrst (in dollars) P = principal (in dollars) R = rat pr annum (as a dcimal) T = tim (in yars). A = P + I whr A = total amount payabl (in dollars). A Instalmnt = --- n whr n = numbr of instalmnts. Tutorial 1 mony CALCULATIONS 21

22 xrcis 1.4 Simpl intrst Prparation: Exrcis Calculat th simpl intrst payabl on a loan of $450 at a rat of 22% p.a. for 3 yars. 2 Calculat th simpl intrst in ach of th following cass. (a) P = $440, R = 0.08, T = 5 yars (b) P = $60, R = 0.09, T = 7 yars (c) P = $369, R = 0.12, T = 3 yars (d) P = $60, R = 8.5%, T = 2 yars () P = $3800, R = 16.8%, T = 3.5 yars (f) P = $1500, R = 12.1%, T = 2.5 yars 3 What is th total amount to b rpaid on a loan of $8150 ovr 3 yars and 6 months at 18.5% p.a.? 4 Choos th corrct answr. Th simpl intrst on $870 for 4 yars at 15% p.a. is: A $ B $ C $ D $ $870 E $ Choos th corrct answr. Th total amount to b rpaid on a loan of $520 ovr 2 months at 12.4% p.a. is: 2 A $ $520 B $ $ C 2 2 $ $520 D $ E 2 $ Writ two diffrnt sts of valus for P, R and T that would rsult in simpl intrst of $ Calculat th simpl intrst accrud on a sum of $900 at 5.5% p.a. for: (a) 29 days (b) 56 days (c) 8 days (d) 19 days 8 Choos th corrct answr. Th simpl intrst on $378 for 14 days at 6.2% p.a. is: 2 14 A $ B $ C $ D $ E $ How much will b paid out to Sol, who puts $1400 into a bank account paying 6% p.a. simpl intrst if h withdraws th total amount aftr 240 days? (Intrst is paid on daily balancs.) Worksht C Hinmann MATHS ZONE

23 10 Victor agrs to lnd Esm $1500 so that sh can go on a holiday to Fiji. H is to b paid back quartrly, at 12% p.a. simpl intrst, with th dbt to b rpaid in full in 5 yars. Calculat: (a) th total amount payabl (b) th amount of th quartrly instalmnts. 11 Frdrica puts $280 into a bank account paying 7.5% p.a. intrst. Aftr 5 wks sh dposits a furthr $190. How much will sh rciv if sh withdraws th mony 12 wks aftr th first dposit? (Assum 52 wks in a yar.) 12 Calculat th total intrst payabl for th month of Jun on an account that has a balanc of $750 for 10 days, a balanc of $1050 for 12 days and a balanc of $500 for th rst of Jun, if th account pays 6.6% p.a. calculatd: (a) daily (b) on th minimum monthly balanc. 13 (a) Calculat th intrst payabl for th month of April on an account that pays 5.8% p.a. intrst, and has a balanc of $155 for 3 days, $820 for 19 days and $580 for th rst of th month, if th intrst is paid on: (i) th minimum monthly balanc (ii) th daily balanc. (b) How much mor is th intrst in part (ii) than in part (i)? 14 A statmnt for an account offring 6.9% p.a. shows th following for th month of July. July Transaction Balanc Balanc Withdrawal Dposit $170 $450 $350 $180 $630 How much intrst is payabl for July if intrst is calculatd: (a) daily? (b) on th minimum monthly balanc? 15 A statmnt for an account offring 7.4% p.a. shows th following for th month of Novmbr. Novmbr Transaction Balanc Balanc Dposit Withdrawal $285 $207 $100 $385 $178 How much intrst is payabl for Novmbr if intrst is calculatd: (a) daily? (b) on th minimum monthly balanc? 1 mony CALCULATIONS 23

24 16 A statmnt for an account offring 7.8% p.a. shows th following for th month of Dcmbr. Dcmbr Transaction Balanc Balanc Dposit Withdrawal Withdrawal $530 $260 $300 $65.20 $ $ $35.20 How much intrst is payabl for Dcmbr if intrst is calculatd: (a) daily? (b) on th minimum monthly balanc? Qustions Using itration to invstigat savings plans It may b hlpful to work on this invstigation with a partnr. In mathmatics, itration occurs whn th output from a mathmatical rul bcoms th input to th rul th nxt tim th rul is procssd. Considr th rul of doubling a numbr and taking away 10. If th first input is 20, th rul bcoms and th output is 30. Th output now bcoms th nxt input. That is, w apply th rul to 30. Th scond output is 50, i = 50. Each tim w go through th procss w say an itration has bn prformd. Th first itration gav a rsult of 30 and th scond itration gav a rsult of 50. Th diagram blow shows how itration works. First input Input Mathmatical rul For xampl: 2 Input 10 Output To prform this itration on th graphics calculator, prss 2 0 and thn prss th ENTER or EXE ky. This stors 20 into th calculator s Ans variabl. Ans is short for Answr and always holds th valu of th last answr. Prss ENTER. Prss ENTER again. Your scrn should b similar to th on shown in th display on th right. Each tim th ENTER or EXE ky is prssd an itration of th rul Ans*2-10 is prformd on th valu stord in Ans. Find th valus of th third, fourth, fifth and tnth itrations. 24 Hinmann MATHS ZONE

25 Suppos you ar abl to sav $1200 ach yar towards a major holiday in 10 yars tim. You hav to choos th bst plan from th options blow: Plan Paymnt* Intrst rat Plan A: Rgular Savr $100 pr month 9% p.a. paid monthly Plan B: Priodical Savr $600 pr six months 10% p.a. paid six-monthly Plan C: Yarly Lump Sum $1200 pr yar 9% p.a. paid yarly * All paymnts commnc at th bginning of th priod. Invstigating Plan A: Rgular Savr Calculat th monthly rat of intrst. Dividing 9% p.a. by 12 givs a rat of 0.75% pr month or pr month as a dcimal rat. Th amount savd at th bginning of th scond month is calculatd as follows: Initial dposit = $100 Intrst on dposit = $100 = $0.75 Scond dposit = $100 Total = $( ) = $ Th amount savd at th bginning of th third month is calculatd as follows: Prvious balanc = $ Intrst on balanc = $ $1.51 Third dposit = $100 Total = $( ) = $ To prform th calculations abov, ntr th xprssion as shown in th scrn display. Prss ENTER or EXE. Th answr, , is th amount savd at th bginning of th scond month. 1 Explain what ach part of th xprssion Ans+(0.09/12)*Ans+100 dos. 2 Prss ENTER or EXE again. Th calculator computs th valu of Ans+(0.09/12)*Ans+100 but uss th valu for Ans. Th valu displayd is th amount savd at th bginning of th third month. Dos it agr with th valu obtaind arlir? 3 Copy th tabl blow into your workbook. By prssing th ENTER or EXE ky, complt th tabl for Plan A. Bginning of month Amount savd ($) Extnd th tabl to find th amount savd at th bginning of ach yar for yars 4 to 11 inclusiv of th savings plan. : Th nd of th tnth yar occurs at th bginning of th lvnth yar. This happns at th bginning of th 121st month. 1 mony CALCULATIONS 25

26 5 How much is savd at th nd of tn yars if th paymnt of $100 at th bginning of yar 11 is not includd? Invstigating Plan B: Priodical Savr To calculat th six-monthly rat of intrst, divid 10% p.a. by 2. This givs a rat of 5% pr six months or 0.05 pr month as a dcimal rat. At th bginning of th scond six-month priod th amount savd is calculatd as: Initial dposit = $600 Intrst on dposit = 0.05 $600 = $30 Scond dposit = $600 Total = $( ) = $1230 In your workbook, copy and complt th calculation blow for th bginning of th third six-month priod. Prvious balanc = $ Intrst on balanc = 0.0 $1230 = $.50 Third dposit = $600 Total = $( ) = $.50 Entr th xprssion as shown in th scrn display. Prss ENTER or EXE. Th answr, , is th amount savd at th bginning of th scond six-month priod. 1 Explain what ach part of th xprssion Ans+(0.1/2)*Ans+600 dos. 2 Prss ENTER or EXE again. Th valu displayd is th amount savd at th bginning of th third six-month priod. Dos it agr with th valu obtaind arlir? 3 Copy and complt th tabl for Plan B. Bginning of six-month priod Amount savd ($) Continu th tabl to find th amount savd at th bginning of ach yar for yars 2 to 11 inclusiv of th savings plan. 5 How much is savd at th nd of 10 yars if th paymnt of $600 at th bginning of yar 11 is not includd? Invstigating Plan C: Yarly Lump Sum Us th itration mthods shown to find th amount savd at th bginning of ach yar from yars 1 to 10 and at th nd of th tnth yar. Assum that th nd of th tnth yar is th sam as th bginning of th lvnth yar but dos not includ th lvnth yar paymnt. Comparing th plans Writ a brif rport that compars th plans and th amount savd in ach plan aftr tn yars. Which plan would you rcommnd? How practical ar th plans? 26 Hinmann MATHS ZONE

27 Carlss Carly Carly is givn a savings account by hr parnts with som mony alrady dpositd into it. Carly is trying to avoid withdrawing mony from th account but is not vry good at sticking to hr plans. Soon sh raliss that sh has alrady withdrawn as much mony as thr is rmaining in th account. Th nxt wk Carly withdraws anothr $m and raliss that th ratio of withdrawn mony to mony rmaining is now 3 : 2. What will b th ratio of withdrawn mony to mony rmaining if Carly withdraws anothr $m. Equations can b usful hr, or mayb trial and rror. Intrst-fr Thr ar a numbr of paymnt options opn to popl whn purchasing goods. Apart from cash transactions, customrs can us EFTPOS (Elctronic Funds Transfr at Point Of Sal) and dbit cards. Ths ar similar to paying with cash in that thy don t hav any intrst fs and rquir th financ to b availabl at th tim of purchas. Bank fs ar oftn chargd for ths kinds of transactions. Chqus hav bn usd as a rplacmnt for cash for a long tim but ar dcrasing in popularity for a numbr of rasons, such as fs chargd by banks for chqu facilitis. Businsss ar wary of prsonal chqus bcaus thr is no way of knowing if th customr actually has th mony, whras bank chqus ar scurd. Whn you purchas an itm with lay-by th stor holds th itm whil you mak paymnts. You rciv th itm aftr it has bn compltly paid for. No intrst is chargd, although an initial paymnt, or dposit usually calculatd as a prcntag of th valu of th itm is rquird immdiatly. Dfrrd paymnt is a trm mostly usd to dscrib on of th paymnt options for HECS (Highr Education Contribution Schm). It is a govrnmnt loan for which rpaymnts commnc whn th borrowr arns abov an amount st by th govrnmnt. Rpaymnts ar calculatd as a prcntag of th borrowr s taxabl incom. 1 mony CALCULATIONS 27

28 workd xampl 16 Joanna uss EFTPOS for most of hr purchass. Hr bank chargs 50 cnts pr EFTPOS transaction as wll as a $2 account-kping f pr month. If Joanna maks 12 EFTPOS purchass in on month, what amount will hr bank charg hr? Stp Add th transaction chargs to th account-kping f. Solution Fs = 12 $ $2 = $6 + $2 = $8 workd xampl 17 Christi wantd to buy a particular pair of jans for $130 but didn t hav nough mony, so sh dcidd to lay-by thm. Th stor rquirs a dposit of 20%. (a) How much did Christi pay to bgin th lay-by? (b) If Christi pays off $20 pr wk, how long will it b until sh owns th jans? Stps (a) Find th rquird prcntag of th cost of th itm. (b) 1. Find th balanc by subtracting th dposit from th cost of th itm. 2. Find how many tims th rgular paymnt gos into this amount. 3. Intrprt th answr. (Any rmaindr will tak an xtra wk to pay off.) Solutions (a) Dposit = 20% of $130 = 0.2 $130 = $26 (b) Balanc = $130 $26 = $104 $104 $20 = 5.2 Christi will tak 6 wks to pay off hr lay-by. Intrst pnaltis Crdit cards hav significantly rducd th us of chqus. Thr ar many diffrnt conditions undr which crdit cards oprat. Som hav an intrst-fr priod of 25 or 30 days aftr th billing priod nds. Som hav a significant annual f whil othrs hav no f. Crdit cards can b a vry usful mod of paymnt, but car nds to b takn not to xcd th intrst-fr priod too much as th intrst chargd is at a substantial rat, usually btwn 12% and 17%. Simpl intrst is thn calculatd on th amount owd back to th dat of purchas and addd onto th total amount owd at th nd of th billing priod. You r a crdit to m. I m proud of you! 28 Hinmann MATHS ZONE

29 Buying on trms is somtims calld hir purchas.this mans you tak possssion of th itm bfor it has bn paid off. Many stors offr an intrst-fr priod whr you ar rquird to pay a small account administration f on top of your paymnts for th itm, with no intrst chargd during that priod. Howvr, if you don t manag to pay for th itm bfor this priod finishs, th intrst rats chargd ar vry high, usually btwn 22% and 30%. Oftn th intrst is thn chargd to covr what was calld th intrst-fr priod. Banks and financ companis offr prsonal loans for cars, furnitur, travl and a numbr of othr itms. Taking out a loan can b a bttr option bcaus th intrst rats ar lowr, usually btwn 9% and 12%. workd xampl 18 Taz has a crdit card that has no intrst-fr priod and chargs an annual intrst rat of 13.85%. Find th amount of intrst chargd on a purchas of $ if th full dbt is rpaid 21 days latr. Stps Solution 1. Idntify P, R and T. P = $ R = 13.85% = T = Writ th simpl intrst formula. I = PRT 3. Substitut and calculat. = $ $ workd xampl 19 Calculat th total intrst payabl at th du dat for th following st of crdit card transactions. Th card has no intrst-fr days and chargs an annual rat of 13.95%. Statmnt dat: 5 Octobr Opning balanc: $0.00 Transaction dat Amount ($) 5 Sptmbr 11 Sptmbr 25 Sptmbr 3 Octobr Du dat: 30 Octobr This statmnt covrs th priod: 3 Sptmbr to 5 Octobr mony CALCULATIONS 29

30 Stps 1. Idntify P, th balancs, and th associatd tims, T, convrtd to yars. (Rmmbr: $37.35 is owd for 5, 6, 7, 8, 9, 10 Sptmbr; thn ($ $45.80) is owd for 11 to 24 Sptmbr, tc.) 2. Idntify th rat, and convrt this to dcimal form. Solution Sp: $37.35 for 6 days, i yars Sp: $83.15 for 14 days, i yars Sp 2 Oct: $ for 8 days, i yars Oct: $ for 27 days, i yars 365 R = 13.95% = Writ th simpl intrst formula. I = PRT 6 4. Substitut to find th individual 5 10 Sp: I = amounts of intrst. Writ ths 14 corrct to six dcimal placs Sp: I = Sp 2 Oct: I = Oct: 27 I = Calculat th total intrst. Total intrst = Writ this corrct to th narst cnt. $3.29 As th nam suggsts, many popl us crdit cards as a lin of crdit. Thy do not pay th total amount owing at th nd of ach month. Th financial institution that has issud th card will hav a formula to work out what is known as th minimum amount du.this formula consists of two parts, such as $10 or 5% of th amount outstanding, whichvr is th gratr. workd xampl 20 Tylr s financial institution rquirs hr to pay ach month a minimum of $20 or 5% of th outstanding balanc, whichvr is th gratr, off hr crdit card. Find th paymnt du if Tylr s amount outstanding is: (a) $240 (b) $899 Stps (a) 1. Find th statd prcntag of th amount owing. 2. Dcid which is gratr, $20 or th 5% calculation. (b) 1. Find th statd prcntag of th amount owing. 2. Dcid which is gratr, $20 or th 5% calculation. Solutions (a) 5% of $240 = 0.05 $240 = $12 Tylr will pay $20. (b) 5% of $899 = 0.05 $899 = $44.95 Tylr will pay $ Hinmann MATHS ZONE

31 workd xampl 21 Dominic is intrstd in purchasing a nw loung suit. H has sn on advrtisd for $2799, but fls h can only afford to part with $300 at th momnt. Th stor offrs Dominic a 12-month intrst-fr plan whr h must pay 10% of th cost up-front. H must also pay a $20 application f plus a $2.50 account-kping f pr month. (a) If Dominic pays off th loung suit within th 12 months, how much dos h pay in total? (b) If Dominic cannot pay th loung suit off within th 12 months h will b chargd 29% p.a. on th amount rmaining for th 12 months h had intrst-fr. Aftr 12 months, Dominic has not paid off $1000. What will this amount incras to? Stps (a) Add th application f and th account-kping fs to th cost of th loung suit. (b) 1. You will b using th simpl intrst formula, so dfin P, R and T. Solutions (a) Total cost = $ $20 + $ = $ $20 + $30 = $2849 (b) P = $1000 R = 29% = 0.29 T = 12 months = 1 yar 2. Writ th formula. I = PRT 3. Substitut and calculat. = $ = $ Find th total amount owing by adding th intrst to th amount not yt paid off. A = P + I = $ $290 = $1290 xrcis 1.5 Paymnt mthods Prparation: Exrciss 1.1, A bank chargs a monthly account-kping f of $4 for its Easy Savr account. EFTPOS transactions ar chargd at $0.75 pr transaction. Calculat th monthly f chargd if th numbr of EFTPOS transactions is: (a) 0 (b) 2 (c) 8 (d) 15 2 Th following itms wr purchasd using lay-by. If th stor rquird 20% of th cost of th itm as a dposit, find for ach itm (i) how much th dposit was and (ii) how many wks it took to pay th itm off. (a) a $90 jackt with wkly paymnts of $15 (b) a $45 jumpr with wkly paymnts of $10 (c) a $300 tnt with wkly paymnts of $40 (d) a $170 dsk with wkly paymnts of $30 hi.com.au 1 mony CALCULATIONS 31

32 3 Suzann and Dzung ar trying to dcid which mthod thy should us to pay thir rnt of $950 ach month. Thy can withdraw cash from thir account using an ATM, thn go into a bank to dposit it into thir landlord s account; or thy can post a chqu to thir landlord s workplac. (a) Th ATM will only allow withdrawals of up to $400 ach tim, at a cost of $1 pr withdrawal. How much would it cost to withdraw th $950 from th ATM? (b) Suzann s bank chargs $6 pr chqu. How much would sh hav to spnd on chqus for rnt in on yar? 4 Find th amount of intrst paid on ach of th following crdit card purchass. Th cards hav no intrst-fr priod. (a) $ rpaid fully in 22 days, intrst rat 15.5% p.a. (b) $ rpaid fully in 10 days, intrst rat 22% p.a. (c) $ rpaid fully in 17 days, intrst rat 17% p.a. (d) $ rpaid fully in 19 days, intrst rat 14.25% pa. () $ rpaid fully in 28 days, intrst rat 17.75% p.a. (f) $ rpaid fully in 20 days, intrst rat 16.3% p.a. 5 Choos th corrct answr. Ramona has a crdit card with an annual intrst rat of 14.25% and no intrst-fr priod. Th amount of intrst on a purchas of $ fully rpaid in 17 days is closst to: A $0.82 B $2.99 C $1.09 D $10.91 E $ Calculat th total intrst payabl at th du dat for ach of th following sts of crdit-card transactions. Th card has no intrst-fr days and chargs an annual rat of 13.95%. (a) Statmnt dat: 3 Jun Opning balanc: $0.00 (b) Statmnt dat: 5 August Opning balanc: $0.00 Transaction dat 12 May 25 May 1 Jun Du dat: 28 Jun Amount ($) Transaction dat 4 July 19 July 31 July 2 August Du dat: 30 August Amount ($) This statmnt covrs th priod: 5 May to 3 Jun This statmnt covrs th priod: 3 July to 5 August 32 Hinmann MATHS ZONE

33 7 Find th minimum paymnt du on ach of th following monthly crdit card balancs if th financial institution rquirs a minimum paymnt of $25 or 7.5% of th amount outstanding, whichvr is th gratr. (a) $250 (b) $192 (c) $950 (d) $835 () $400 (f) $ (a) Your financial institution rquirs a minimum paymnt on your crdit card of $20 or 5% of th amount outstanding, whichvr is th gratr. Find th amount outstanding if th prcntag calculation is qual to $20. (b) Find th amount outstanding if th conditions ar $30 or 7.5% of th balanc outstanding and ths amounts ar qual. 9 Eryn s financial institution rquirs that sh pay $30 or 8% of th balanc outstanding on hr crdit card, whichvr is th gratr. (a) If hr latst statmnt asks for a $30 paymnt, giv thr possibl valus for th amount outstanding on Eryn s crdit card. (b) For ach of th amounts in part (a), calculat th intrst chargd if Eryn pays th amount off in 17 days at 18% p.a. 10 John wants to buy a tlvision valud at $850. H dosn t hav nough mony at th momnt and is offrd a 6-month intrst-fr dal whr no upfront paymnt is rquird. John has to pay a $25 application f and an account-kping f of $3 pr month. (a) If John pays for th tlvision within 6 months, how much dos h pay altogthr? (b) If John still ows $200 at th nd of th 6 months, how much will this amount incras to if th intrst rat is 26% p.a. chargd for th prvious 6 months? 11 Itms worth th following amounts ar purchasd with 12 months intrst-fr. A 10% dposit is rquird, as wll as a $25 application f. An account-kping f of $2.50 pr month is anothr cost incurrd. For ach itm find (i) th dposit rquird and (ii) th total amount paid if th itm is paid off in 12 months. (a) $1000 (b) $650 (c) $1200 (d) $ Jong-Mun has a HECS dbt for this smstr of $2563. (a) If Jong-Mun pays up-front h only has to pay 75% of th total dbt and th govrnmnt pays th rst. How much will Jong-Mun hav to pay if h chooss this option? (b) Jong-Mun dcids h may b abl to pay $1000 off th dbt. As an ncouragmnt to popl to pay lump sums lik this, th 4 govrnmnt subtracts -- of th actual amount paid from th dbt. 3 (i) How much will Jong-Mun s dbt b rducd by if h pays $1000 up-front? (ii) What will Jong-Mun s dfrrd amount b? 1 mony CALCULATIONS 33

34 13 Gary dcidd to dfr his total HECS amount. At th nd of his dgr h owd th govrnmnt $ in HECS fs. In his first yar out of univrsity, Gary has an annual salary of $ This is also his taxabl incom amount. Th govrnmnt will dduct 4.5% of this for HECS. (a) (i) How much HECS will b dductd from Gary s pay this yar? (ii) What will his HECS dbt b rducd to? (b) Gary s incom incrass th nxt yar, so h is rquird to pay 5.5% of $ in HECS. How much HECS will b dductd from Gary s pay this yar? (c) If Gary continus to pay off that amount in HECS ach yar, how many mor yars will it tak for Gary to hav no HECS dbt rmaining? Round your answr up to th nxt half-yar. 14 Kvin wants to purchas houshold appliancs worth $1800, $2400 and $900. Each applianc is offrd to Kvin for 12 months intrst-fr. H is chargd a $25 application f for ach applianc as wll as account-kping fs of $2 pr month for ach of th thr accounts. (a) If all thr appliancs ar paid off within 12 months, how much will Kvin hav paid in total? (b) Kvin dosn t think h can pay off all thr appliancs in 12 months. If Kvin still ows $2000 in total at th nd of th 12 months, what will this amount incras to if th intrst rat is 28.6% p.a. chargd on th prvious 12 months? (c) Kvin dcids that gtting a small prsonal loan may b a bttr option. If h borrows $5000 for 3 yars and is chargd 10.6% p.a. simpl intrst, how much will h ow at th nd of th 3 yars, assuming that no rpaymnts ar mad during this tim? 34 Hinmann MATHS ZONE

35 Purchasing a car Martin and Dirdr ar in th markt for a car. Thy s th advrtismnt for th typ of car thy ar intrstd in purchasing. $ $70.15 pr wk Closr inspction of th advrtismnt rvals that th paymnts ar for four yars and a 35% dposit is rquird. 1 How much dposit do Martin and Dirdr nd to pay? 2 How much, in total, will thy pay for th vhicl undr ths arrangmnts? Martin and Dirdr dcid to chck out anothr option for financing thir purchas. Thy find that thy can gt a loan from a frind at a fixd simpl intrst rat of 10.95% p.a. for four yars. Thy dcid to pay th 35% dposit from thir savings. 3 Find how much, in total, thy will pay for th vhicl undr ths conditions. 4 What wkly paymnt will thy nd to mak to thir frind? 5 What will th maximum possibl intrst rat on th loan from th frind nd to b to mak th total car cost lss than if thy purchas th car by making th wkly rpaymnts through th car yard? 1 mony CALCULATIONS 35

36 A discount is a rduction in th markd pric of an itm. It may b offrd whn a stor is ovrstockd or at th nd of th sason. Establishd clints ar oftn givn spcial discounts, and rductions can b mad for purchass in bulk to ncourag high-volum sals. Tradspopl can gt discounts in thir trad ara for xampl, carpntrs gt discounts on timbr. Th aim of a discount is to ncourag potntial customrs to buy. workd xampl 22 Bullsy Stor advrtiss a summr claranc sal in which all itms of clothing ar discountd by 25%. How much will a shirt markd $46 sll for at th sal? Stps W will show two diffrnt mthods. 1. Find th discount (D) from th markd pric (MP). 2. To find slling pric (SP), subtract th discount from th markd pric. 1. Calculat th prcntag of th pric that is rtaind. Solution Indirct mthod D = 25% of MP = 0.25 $46 = $11.50 SP = MP D = $46 $11.50 = $34.50 Dirct mthod 100% 25% = 75% 2. Find th slling pric. SP = 75% of MP = 0.75 $46 = $34.50 Discounts Indirct mthod: Slling pric = markd pric discount i.. SP = MP D whr D = %D MP Dirct mthod: Slling pric = prcntag rtaind markd pric i.. SP = %SP MP whr %SP = 100% %D 36 Hinmann MATHS ZONE

37 xrcis 1.6 Discounts 1 Calculat th amount of discount on ach of th following itms and hnc find th slling pric (indirct mthod). (a) a $60 pair of jans discountd by 20% (b) a $54 shirt discountd by 30% (c) a $24 ti discountd by 15% (d) a $360 suit discountd by 12.5% 2 Calculat th slling pric of ach of ths itms dirctly (dirct mthod). (a) a $24 pair of shorts discountd by 15% (b) a $64 skirt discountd by 40% (c) a $6 pair of socks discountd by 30% (d) a $420 vning gown discountd by 37.5% 3 Choos th corrct answr. Th slling pric of a parka markd at $36 aftr a discount of 23% is: A $( ) B $(36 23) C $( ) D $( ) E $ Choos th corrct answr. Th slling pric of a swatshirt markd at $28 aftr a discount of 16% is: A $ B $ C $( ) D $ E $( ) 5 A buildr buys $840 worth of timbr to build an xtnsion. If h is allowd a 12.5% discount, how much dos h pay? 6 A drssmakr buys 20 m of matrial at $5.98 pr mtr. If sh gts a 15% discount, how much dos sh pay? 7 A purchasing cooprativ gts a discount of 24% on grocris bought in bulk. How much do thy sav on $370 worth of grocris? 8 A jackt markd at $295 is still in a shop at th nd of wintr. Prdict thr possibl prcntag discounts that might b offrd ovr th nxt fw wks and th slling pric that would rsult for ach discount. Prparation: Exrcis A fruit stall oprator starts th day with 100 kg of appls slling at $3.90 pr kg. Whn thr ar only 20 kg lft, sh offrs a 40% discount. (a) What is hr slling pric pr kilogram now? (b) What is th total slling pric of th 100 kg of appls? Tstr Worksht C1.2 Homwork mony CALCULATIONS 37

38 Whnvr invstmnt of any kind taks plac thr is th potntial for a profit or a loss to occur. A profit occurs whn th invstmnt incrass in valu. A loss occurs whn th invstmnt dcrass in valu. To calculat th prcntag profit,w xprss th profit as a fraction of th cost pric, thn multiply by 100, attaching th % symbol. If thr is no profit or loss, w say w brak vn. whr profit % profit = % CP Profit = slling pric cost pric = SP CP If SP CP, thn SP CP will b ngativ. W intrprt this as a loss. workd xampl 23 A hi-fi systm costs an lctrical stor $950. It slls th systm for $1250. Calculat th prcntag profit, corrct to two dcimal placs. Stps Solution 1. Calculat th profit. Profit = SP CP = $( ) = $300 profit 2. Find th profit as a prcntag of th cost % profit = % CP pric. $300 = % $ % Slling pric can b found dirctly from cost pric if th prcntag profit is known. SP = R CP whr R, th profit factor = 100% + % profit 38 Hinmann MATHS ZONE

39 workd xampl 24 A rtail stor has a policy of slling its mrchandis so that th prcntag profit is 65%. What would a sofa that cost th stor $300 b sold for? Stps Solution 1. Writ down th formula. SP = R CP 2. Calculat R. R = 100% + % profit = 100% + 65% = 165% = Find th slling pric. SP = 1.65 $300 = $495 xrcis 1.7 Profit and loss 1 Calculat th prcntag profit or loss in ach cas. (a) CP = $45, SP = $54 (b) CP = $360, SP = $468 (c) CP = $4500, SP = $ Choos th corrct answr. If a tabl cost $486 and was subsquntly sold for $448, th prcntag profit or loss was: A ( ) 100 ( ) % profit B % profit C ( ) 100 ( ) % loss D % loss E ( ) % loss Calculat th slling pric if: (a) CP = $48, prcntag profit = 45% (b) CP = $60, prcntag profit = 60% (c) CP = $420, prcntag profit = 24% (d) CP = $4890, prcntag profit = 28% Prparation: Exrcis Writ thr pairs of valus for CP and SP, ach of which rsults in 35% profit. 5 A stallholdr at th wknd markt buys 10 kg of brokn chocolat pics for $45. Sh puts thm into smallr plastic bags of 250 g and slls thm for $1.50. Find th prcntag profit corrct to on dcimal plac. Worksht C1.3 1 mony CALCULATIONS 39

40 6 A hamburgr stallholdr buys rolls for $4 pr dozn, and bf pattis for $9 for 20. Th sauc costs 2 cnts pr hamburgr, and nough onions for a dozn hamburgrs cost $2. Calculat th prcntag profit, corrct to on dcimal plac, if th hamburgrs ar sold for $ A kn cyclist buys a bicycl through th Trading Post for $40 for hr daughtr. Sh spnds an additional $35 in parts and latr slls th bicycl for $100. If th cost of th advrtismnt to sll is $10, calculat hr profit as a prcntag of hr total outlay, corrct to on dcimal plac. Oftn, as customrs, w can s only th final pric that is paid, aftr profits ar addd, commissions calculatd and discounts allowd. Th following approach allows us to rvrs th procsss w hav bn using to find th original amount. workd xampl 25 A Bucktwar hostss arns commission at th rat of 5.75% on sals of canistrs. How much will sh nd to sll in ordr to mak $200? Stps Solution 1. Convrt th prcntag to a dcimal. 5.75% = Writ th commission formula. C = R SP 3. Substitut known information. $200 = SP 4. Solv for SP. $200 SP = $ Hinmann MATHS ZONE

41 workd xampl 26 A small businss has a policy of aiming for 75% profit on all itms. What was th cost pric of a vas sold for $56? Stps Solution 1. Writ down th formula. SP = R CP 2. Convrt th prcntag profit to th profit factor, R (in dcimals). R = 100% + % profit = 100% + 75% = 175% = Substitut known information. $56 = 1.75 CP 4. Solv for CP. $56 CP = 1.75 = $32 workd xampl 27 A vido rcordr has a sal pric of $450 aftr a discount of 20% is subtractd. What was th original markd pric of th rcordr? Stps Solution 1. Find th prcntag rtaind. 100% 20% = 80% 2. Writ th dirct way to find th slling pric. SP = 80% of MP 3. Substitut known information. $450 = 0.8 MP 4. Solv for MP. $450 MP = = $ Using th simpl intrst formula, it is possibl to calculat R, T or P if th valus of th othr thr variabls ar known. 1 mony CALCULATIONS 41

42 workd xampl 28 Allan, on his rtirmnt, put $ into a cash managmnt account. H rcivd $ whn h withdrw all of th mony 9 months latr. What was th avrag rat of rturn p.a. on his capital (corrct to on dcimal plac)? Stps Solution Writ th givn information in symbols. P = $12 500, A = $ , T = = Calculat th simpl intrst. A = P + I $ = $ I I = $ $ = $ Calculat th intrst rat. I = PRT 3 4. Convrt to a prcntag corrct to on dcimal plac. $ = $ R -- 4 R = $ $ % p.a xrcis 1.8 Mor prcntag calculations Prparation: Prp Zon Q8 and Exrciss 1.2, 1.4, 1.6, Ursula rcivs 5.5% commission on sals of Swdish stainlss stl cooking utnsils. How much worth of cookwar must sh sll in a wk so that hr commission will b: (a) $137.50? (b) $750? (c) $450? (d) $390? 2 A hardwar stor has th policy of marking up its goods by 85%. Calculat th cost pric of an itm sold for: (a) $3.70 (b) $51.00 (c) $ (d) $ An lctrical bulk stor buys a quantity of diffrnt brands of transistor radios. What prics should thy b markd at if th stor intnds to obtain th following prics for thm at th nd-of-summr sal at a 15% discount? (a) $34 (b) $51 (c) $78 (d) $67 4 Choos th corrct answr. To mak $420 pr wk, on 3.5% commission on sals, Jak must sll goods to th valu of: $420 $420 $420 A $ B C D E $ Choos th corrct answr. If a TV st is sold for $840 at a 65% profit, th cost of th st was: $ A $( ) B $ C D $ E $( ) Worksht C Hinmann MATHS ZONE

43 6 Choos th corrct answr. If a dsk is for sal for $140 aftr a 25% discount, this mans that it was originally markd at: A $175 B $245 C $560 D $16 E $ Choos th corrct answr. If R = 0.09, P = $400, I = $43.80, thn T (in yars) = A B C D E Choos th corrct answr. If P = $95, T = 4 months, I = $16.20, thn R (as a dcimal) = A B C D E Choos th corrct answr. If R = 5%, T = 3 yars, I = $19, thn P (in dollars) = A B C D E Calculat R,thn writ it as a prcntag (p.a.) to on dcimal plac whn: (a) P = $245, T = 5 yars, I = $110 (b) P = $420, T = 2.25 yars, I = $132 (c) P = $24, T = 5 months, I = $1.15 (d) P = $6542, T = 35 wks, I = $ Calculat T (in yars) corrct to on dcimal plac whn: (a) P = $245, R = 0.06 p.a., I = $116 (b) P = $120, R = 0.07 p.a., I = $32 (c) P = $20, R = 6.6% p.a., I = $7.05 (d) P = $5547, R = 7.7% p.a., I = $ Calculat P (in dollars) whn: (a) T = 2 yars, R = 0.08 p.a., I = $216 (b) T = 3.5 yars, R = 0.05 p.a., I = $35 (c) T = 4 wks, R = 7.6% p.a., I = $12.45 (d) T = 5 months, R = 4.7% p.a., I = $ Aftr invsting $6000 into a savings account paying 7% p.a. intrst, Ian rcivd $6238. For how many days (corrct to th narst day) was th mony invstd? 14 Aftr invsting $5000 in a fixd dposit for 2 yars for a trip to London, Inika rcivd $5890. What prcntag rturn p.a. did sh gt? 12 Worksht C1.5 1 mony CALCULATIONS 43

44 15 Wrnr put $8000 into a cash managmnt account. H rcivd $ whn h withdrw all of th mony 18 months latr. What was th avrag rat of rturn p.a. on his capital (corrct to on dcimal plac)? 16 (a) If a gift shop buys crystal glasss for $10.50 ach, and wishs to mak a 60% profit, what must thy b sold for? (b) What must th glasss b markd at in ordr for a 20% discount to b offrd if th 60% profit is still mad? 17 A timbr yard buys hardwood at $0.55 pr mtr. If buildrs ar allowd a 17.5% discount and th businss must mak a profit of 45%, at what pric should th timbr b markd? 18 An ncyclopdia salsprson rcivs 8% commission on sals. If th publishr wishs to gt a 45% profit, aftr paying th commission, what must th st of books b sold for if th st cost $560 to publish? 19 Sarina is saving for hr ovrsas trip to Los Angls and nds to hav $540 in 3 months. How much mony must sh invst at 9% p.a. in ordr to arn this amount? 20 Hung arns $640 on an invstmnt of $8000. Giv thr possibl simpl intrst rats as prcntags pr annum, and thir corrsponding tim priods, that could hav producd ths rsults. Do ths in your had as quickly as you can and writ down th answrs $ % of x 7x cm = mm 6 -- of $ = 289, so = Tim targt: 2 minuts 44 Hinmann MATHS ZONE

45 Accountant Gnviv MacDonald Position: Financial Controllr Company: Rd Educational and Profssional Publishing Australia Qualifications/Exprinc: Bachlor of Businss (Accounting) Monash Univrsity (3 yars), 1 Crtifid Practising Accountant (2 -- yars) 2 Rlatd occupations: Financial plannr, stockbrokr, conomist, businss analyst I manag th financial information of Rd Education, th Australian branch of a larg multinational publishing company. Accountancy has two sids: complianc, and valu-adding. Complianc mans that I mak sur that vrything w do is within th Australian corporat tax accountancy rgulatory framwork. Th valu-adding part of th job involvs analysing data about th businss as a whol and what drivs th businss to grow and mak mony. This mans looking at th big pictur rathr than just th fin dtails. I think maths tachs you to think in a logical mannr. My favourit parts of maths at school wr logic, ratios, prcntags, algbra, intgrs and statistics. I us all of ths in my job. Although I dvlop spradshts to do most of my calculations automatically, I nd to hav a good undrstanding of th formula undrlying th calculations to st up ths spradshts. On common problm involvs calculating th pric that Rd should charg for a book, givn th cost of its production and th lvl of profit rquird by th company. Suppos w publish 1000 books, which w nd to sll for a rquird profit of $5000. Th cost of producing th books is $7000, and w offr a discount to our buyrs of 7.5%. My task is to find out what th rcommndd rtail pric (rrp) of th book should b. For xampl, if a book is sold at a discount of 7.5%, th amount of mony that th company rcivs for ach book is 92.5% of rrp. For 1000 books sold, this givs us rvnu = 92.5% 1000 rrp; rquird profit = $5000; cost = $7000. Sinc profit = rvnu from th books cost of producing th books w substitut in th valus abov to gt $5000 = 92.5% 1000 rrp $7000 $5000 = 925 rrp $ rrp = $ rrp $12.97 (roundd to two dcimal placs) Th rcommndd rtail pric of th book should b $ Th accountant s problm Gnviv s company wants to publish 2000 books, which it nds to sll for a profit of $8000. Th cost of producing th books is $13 000, and it offrs a discount to buyrs of 9.5%. What should th rcommndd rtail pric (rrp) of th book b? 1 mony CALCULATIONS 45

46 Answr th qustions (to th narst dollar), showing your working, thn arrang th lttrs in th ordr shown by th corrsponding answrs to find th cartoon caption. Us th tabl on pag 16 to find th tax payabl on ach of ths taxabl incoms: O $ U $ A $ N $ Find th simpl intrst arnd with ach of ths trm dposits: A principal = $4000, rat of intrst = 5%, tim = 3 yars C principal = $55 000, rat of intrst = 7.1%, tim = 8 yars T principal = $8900, rat of intrst = 6.5%, tim = 10.5 yars C principal = $14 500, rat of intrst = 8.2%, tim = 15 yars Find th initial amount invstd in ach of ths trm dposit accounts: N simpl intrst = $3660, rat of intrst = 6%, tim = 5 yars T simpl intrst = $591, rat of intrst = 4.3%, tim = 30 months N simpl intrst = $13 032, rat of intrst = 8%, tim = 9 yars A simpl intrst = $2090, rat of intrst = 7.6%, tim = 12.5 yars $ $ $600 $ $ $4422 $2193 $ $6074 $2200 $ $ Hinmann MATHS ZONE

47 It is oftn a good ida to shop around to find th bst pric or dal on an itm. Evn on your suprmarkt shlvs thr ar usually a fw itms to choos from and your choic may dpnd on pric, quantity or quality. workd xampl 29 Giulia nds to purchas a jar of olivs. Thr ar thr diffrnt jars of hr favourit brand on th shlvs at th suprmarkt. Th 700 g jar costs $3.50, th 450 g jar costs $2.20 and th 300 g jar costs $1.90. Which siz jar offrs bst valu for mony? Stps 1. Work out th cost pr gram of ach siz jar. Solution 700 g jar cost pr gram 350 cnts = g = 0.5 cnts pr gram 450 g jar cost pr gram 220 cnts = g cnts pr gram 300 g jar cost pr gram 190 cnts = g cnts pr gram Th smallst numbr of cnts/g gav th bst buy. W could hav workd out g/cnt instad. Th largst valu would thn giv th bst buy. 2. Intrprt th rsults. Th 450 g jar rprsnts th bst valu for mony at about cnts pr gram. For som products thr is incrasing comptition btwn companis for customrs. This can rsult in bttr dals for customrs, but rsarch is ncssary to dtrmin what th bttr dals ar. Mobil phons ar an xampl of such a product. Thr ar many mobil phon companis trying to gt businss, and th bst plan for th customr will dpnd on th numbr and lngth of calls thy mak of ach typ. workd xampl 30 Gabrill is trying to slct a mobil phon plan. Th tabl shows thr options that sh is intrstd in. Gabrill stimats that sh maks 80 minuts worth of calls pr month. Which plan should sh choos? Plan A B C Monthly cost $20 $35 $50 Pr-paid calls pr month $20 $35 $50 Call rat pr 30 sconds 35c 27c 22c 1 mony CALCULATIONS 47

48 Stps 1. Convrt any valus to common units. 2. Calculat Gabrill s avrag call costs undr ach plan. Solution 80 minuts = 4800 sconds 4800 Plan A: 35c = 35c 160 = 5600c = $ Plan B: 27c = 27c 160 = 4320c = $ Plan C: 22c = 22c 160 = 3520c = $ Dcid on th most suitabl plan. Plan B is th chapst for Gabrill. Plan C has a standard monthly cost of $50, so sh would hav about $15 worth of unusd calls. xrcis 1.9 Bst buys 1 Choos th bst valu for mony from ach of th following groups. (a) a 2 kg jar for $5.70, a 1 kg jar for $3.20 or a 750 g jar for $2.50 (b) an 800 g tin for $1.79, a 425 g tin for $1.04 or a 300 g tin for $0.90 (c) a 2 kg packt for $6.09, a 1.5 kg packt for $4.55 or a 1 kg packt for $3.20 (d) a 750 g box for $3.45, a 550 g box for $2.50 or a 375 g box for $1.58 Prparation: Exrcis A backpackr visits a suprmarkt to buy ric. H finds a 2 kg bag for $2.45, a 1 kg bag for $1.30 and a 500 g bag for $0.97. (a) Which siz bag offrs th bst valu for mony? (b) Th backpackr is going on a hik and rally only wants to carry what h nds. If h nds 1.5 kg of ric, is it chapr for him to buy th 2 kg pack and throw away 500 g, or to purchas smallr packs of ric? 3 A 140 g tin of bakd bans costs 68 cnts. Writ thr othr possibl tin sizs and thir costs so that thy ar of approximatly quivalnt valu to this on. 48 Hinmann MATHS ZONE

49 4 A mobil phon company offrs th following thr plans. Plan A B C Pr-paid calls pr month $15 $25 $35 Call rat pr 30 sconds 41c 38c 35c Th lngth of th call is chargd up to th nxt 30 sconds. Calculat how much th monthly charg would b undr ach plan if th customr was chargd for calls totalling: (a) 15 minuts (b) 40 minuts (c) 75 minuts 5 A tlphon company offrs th following dal: Pay $2 xtra pr month and individual intrstat calls will b cappd at $1.95. (a) Joan maks approximatly 20 intrstat calls pr yar, which cost about $5 ach. How much would sh sav with this dal? (b) Rob maks only 5 intrstat calls pr yar but thy usually cost about $12 ach. How much would h sav with this dal? 6 Roland wants to chang his mobil phon plan. H looks at th calls h maks currntly from his mobil phon to hlp him dcid on th bst plan for him. Plan Pr-paid calls pr month Call rat pr 30 sconds A B C $20 $35 $50 35c 27c 22c For ach of ths plans, a flagfall (an initial charg pr call) of 21 cnts is chargd. (a) In a prvious month Roland mad 45 calls, ach approximatly 1 minut long. Find how much this would cost him undr ach plan. (b) In anothr month Roland mad 80 calls, 50 of 1 minut in lngth and 30 of 30 sconds in lngth. Find how much this would cost him undr ach plan. (c) Roland is planning to b mor slctiv with th calls h maks and h will try to kp thm shortr. H stimats that in th futur h will mak approximatly 30 calls pr month of 30 sconds in lngth. Basd on this stimat, which plan do you think Roland should choos? Show your working and giv a rason for your answr. Homwork mony CALCULATIONS 49

50 Summary To convrt a fraction or dcimal to a prcntag, multiply by 100 and attach th % symbol. a To incras or dcras in th ratio a : b,multiply by --, whr b a : b = nw : old. Earnings Pic work: multiply th numbr of pics by th rat. Commission: total wag = rtainr + commission whr commission = % commission slling pric (C = R SP) Salary: paid as a portion of an annual amount, oftn rgardlss of hours workd. Wags: basd on an hourly rat of pay with ovrtim at a highr rat. Incom tax Gross arnings or pay: a prson s arnings bfor any dductions ar mad. Nt arnings or pay: th amount rmaining aftr tax and othr dductions hav bn mad. PAYG (Pay as You Go): a systm whr th mployr withholds tax from a prson s pay and forwards it to th Fdral Govrnmnt. Suprannuation: a fund of mony put asid from ach pay to b accssd at rtirmnt. Gross incom: all mony arnd or rcivd from businss activitis or invstmnts, bfor tax. Tax rturn: a yarly assssmnt of th actual amount of tax payabl. Taxabl incom = gross incom tax dductions: th part of a prson s incom on which tax is paid. Simpl intrst Principal (P): initial amount borrowd in dollars. Rat (R): intrst as prcnt pr annum (writtn as a dcimal). Tim (T): priod of th loan in yars (may b a fraction). Intrst (I) in dollars: I = PRT Amount (A) to b paid back: A = P + I A Instalmnt = --- whr n is th numbr of qual paymnts. n Paymnt mthods EFTPOS: Elctronic Funds Transfr at Point Of Sal. Dbit card: lik paying with cash. 50 Hinmann MATHS ZONE

51 Chqus: attract a f. Lay-by: initial dposit, no intrst, itm collctd at tim of final paymnt. Dfrrd paymnt HECS (Highr Education Contribution Schm): paid back whn taxabl incom is high nough. Crdit card: intrst chargd ithr immdiatly or aftr an intrst-fr priod. Hir purchas: buying on trms from th sllr. Prsonal loan from a bank or financ company: lowr intrst than buying on trms. Discount Slling pric = markd pric discount (SP = MP D), whr D = %D MP SP = %SP MP,whr %SP = 100% %D Profit and loss Slling pric = cost pric + profit (SP = CP + profit) profit (or loss) % profit (or loss) = % CP SP = %SP CP,whr %SP = 100% + % profit or 100% % loss Bst buy Cost pr kilogram (or similar) is last. Total xpnditur on a dal is last. FAQs Ar taxabl incom and nt arnings (or pay) th sam thing? No. Taxabl incom is th amount of incom from all sourcs lft aftr allowabl tax dductions such as work-rlatd xpnss and donations to charity hav bn mad. Taxabl incom is gnrally only calculatd whn complting a tax rturn at th nd of th financial yar th amount of tax payabl is calculatd from th taxabl incom. Nt arnings (or pay) is what you tak hom rgularly aftr PAYG tax and othr amounts (such as prsonal suprannuation contributions) hav bn mad. How do companis bnfit from offring intrst-fr trms? If th itm is not paid off during th intrst-fr priod, th rat of intrst chargd is vry high. Ths companis mak a larg amount of mony from popl who can t manag to pay thir purchass off in tim. 1 mony CALCULATIONS 51

52 Skills 1 Evaluat th following. (a) 1 1 (b) (c) (d) Evaluat th following. (a) (b) (c) (d) (a) Incras 450 m by 15%. (b) Dcras 60 in th ratio 4 How much would a machinist arn in a wk if sh producd 62 pairs of jans and is paid at th rat of $5.90 pr pair? 5 A casual workr arns $8.45 pr hour working in a suprmarkt. How much will h arn if h works: (a) 7 hours? (b) 12 hours? (c) 3.5 hours? (d) 9.5 hours? 6 Choos th corrct answr. An author rcivs 14% of th wholsal pric of a book. If th book slls for $24.50 wholsal, and 7000 copis ar sold, th author will rciv: A $ B $ C $ D $ E $ Calculat th commission on a hous sold for $ if th ral stat agnt is paid 1.75% on th first $ and 1.5% on th rst. 8 Katrina s gross wkly pay is $ If sh contributs 5% to hr suprannuation fund and 31.5% is withhld as PAYG tax, what is Katrina s nt wkly pay? 9 How much incom tax is payabl on ach of ths taxabl incoms? (Us th tabl on pag 16.) (a) $5900 (b) $ (c) $ Sonia lnds L $4000. Sh is to b paid simpl intrst at th rat of 12% p.a. payabl quartrly, with th dbt to b rpaid in full in 4 yars. (a) Calculat th total amount rpaid. (b) What ar th quartrly instalmnts? 11 Natali purchasd an $80 shirt with lay-by. Sh had to pay a 20% dposit to bgin th lay-by. (a) How much was th initial paymnt? (b) If Natali paid $15 pr wk, how many wks did sh tak to pay off th shirt? 12 Find th minimum paymnt du on a crdit card balanc of $240 if th financial institution rquirs a minimum paymnt of $20 or 8% of th amount outstanding, whichvr is th gratr Hinmann MATHS ZONE

53 13 Andrw is purchasing a couch for $700 intrst-fr for 6 months. H must pay a $20 application f and a $2.50 account-kping f pr month. (a) If Andrw pays for th couch in 6 months, how much will h hav spnt on th couch altogthr? (b) Aftr 6 months Andrw still ows $150. This amount is incrasd by an intrst rat of 28% p.a. chargd on th prvious 6 months. How much dos h now ow on th couch? 14 A paintr is allowd a discount of 25% on bulk paints. How much will b savd on a $45 can of paint? 15 Choos th corrct answr. If a pair of snakrs is sold for $87 at a 45% profit, th cost pric was: A $39.15 B $47.85 C $60 D $56.13 E $ Choos th corrct answr. If R = 6%, T = 3 months, I = $12, thn P = A B C D E Franco is at his local suprmarkt purchasing washing dtrgnt. H can purchas a 1 kg packt for $4.89, a 2 kg packt for $7.54 or a 1.5 kg packt for $5.65. Which packt is chapst pr kilogram? Applications 18 Jnny has a gross wkly arnings of $860 and no othr incom. Sh donats $750 pr yar to rgistrd charitis, and has work-rlatd xpnss totalling $690 annually. (a) What is Jnny s annual gross incom, assuming thr ar 52 wks in a yar? (b) What is Jnny s taxabl incom? (c) How much should Jnny pay in tax pr yar? (Us th tabl on pag 16.) 19 At th nd of hr cours, Diana had a HECS dbt of $ Aftr univrsity sh gts a job with an annual salary of $ This is also hr taxabl incom amount. Th govrnmnt will dduct 5.5% of this for HECS. (a) How much HECS will b dductd from Diana s pay in hr first yar? (b) If Diana rmains on this salary, how many yars will it tak for hr to compltly pay off hr HECS dbt? Round your answr up to th narst half-yar , mony CALCULATIONS 53

54 20 A dposit book of an account offring 7% p.a. has th following ntris for th month of Jun. 1.4 Jun Transaction Balanc Balanc Dposit Withdrawal $285 $207 $100 $385 $178 (a) How much intrst is payabl for Jun if intrst is calculatd: (i) daily? (ii) on th minimum monthly balanc? (b) By how much is th intrst in (i) gratr than in (ii)? 21 Calculat th total intrst payabl at th du dat for th following st of crdit card transactions. Th card has no intrst-fr days and chargs an annual rat of 14.55%. (Assum it is not a lap yar.) Statmnt dat: 5 March Opning balanc: $0.00 Transaction dat Amount ($) 11 Fbruary 21 Fbruary 28 Fbruary Du dat: 31 March This statmnt covrs th priod: 4 Fbruary to 5 March Nicola rpays hr fathr $2835 to covr th amount of mony sh borrowd 15 months ago, plus intrst. If sh pays 4% p.a. in intrst, how much did sh borrow? Calculat, without using a calculator. (a) (b) (c) Solv for x. (a) 7x = 35 (b) 17 x = 30 (c) x + 45 = 10 3 A cub has a sid lngth of 4 cm. Find its volum. 4 Writ th supplmntary angl for ach of th following. (a) 90 (b) 125 (c) 12 5 Simplify ths xprssions. (a) 36p 2 q 60p 2 q (b) 32x 2 + 7xy 12x 18x 2 (c) j + 12j + 0.5j Worksht R1.9 Worksht R1.10 Worksht R1.11 Worksht R1.12 Worksht R Hinmann MATHS ZONE