Interest. Interest. Curriculum Ready ACMNA: 211, 229,

Transcription

1 Inteest Cuiulum Redy ACMNA: 211, 229, 234

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3 INTEREST The whole point of Finnil Mths is to pedit wht will hppen to money ove time. This is so you n e peped y knowing how muh money you will hve ened o need to py fte inteest is dded to n mount of money ove etin mount of time. Answe these questions, efoe woking though the hpte. I used to think: Wht do the tems 'pinipl vlue', 'futue vlue' nd 'inteest' men nd how e they elted? If n inteest te is 11% p, wht does this men? Cn n inteest te only e pe ye? Wht e the thee diffeent types of inteest tes? Answe these questions, fte woking though the hpte. But now I think: Wht do the tems 'pinipl vlue', 'futue vlue' nd 'inteest' men nd how e they elted? If n inteest te is 11% p, wht does this men? Cn n inteest te only e pe ye? Wht e the thee diffeent types of inteest tes? Wht do I know now tht I didn t know efoe? % Inteest Mthletis % 3P Lening SERIES TOPIC 1

4 Bsis When money is invested it gows. The 'ext mount' ened is lled the inteest on the investment. Thee e two diffeent kinds of inteest tht n e ened lled simple inteest nd ompound inteest. Finding Simple Inteest Simple inteest is lso lled 'flt inteest'. The initil mount invested is lled the pinipl. Rememe, inteest is the ext mount ened on the pinipl. The fomul to find simple inteest is: Simple inteest I= PRT Time peiod Pinipl Rte (s deiml) The inteest te is often peentge. In the ove fomul R is the peentge witten in deiml fom, so R = Find the simple inteest if you invest $2500 t te of 5% p (pe nnum) fo 4 yes This mens: P = $2500 = 5% T = 4 yes Fist, R must e found fom R = = 5 = 0.05 Use the ove fomul to find the simple inteest R is deiml I = PRT = ^$ 2500h^005. h^4h = $ 500 This mens fte 4 yes the 'ext mount' ened will e $500, so the totl mount fte 4 yes is: Totl = $ $500 = $3000 Sine R =, this vesion of the fomul ould lso e used: I = P# # T When using this vesion, you don't need to find R septely. Eithe fomul will wok, so use the one you think is esie. 2 % Inteest SERIES TOPIC Mthletis % 3P Lening

5 Bsis Time Peiods The inteest te,, does not hve to e pe ye. It n e pe month, pe week o even dily. It is vey impotnt tht the time peiods nd the te mth! This mens, tht if the te is pe month then the time peiods must e months, o if the te is pe week, then time peiods must e weeks. Othewise the fomuls won't wok. In the exmple on the pevious pge, the time peiods e yes nd the inteest te is p (pe ye), so they mth. Find the simple inteest if you invest $0 t n inteest te of 10% pe month fo 2 yes Notie tht the inteest te is in months nd the time peiods e in yes. These do not mth! We hve two options: Method 1: Convet the time peiods to months. Method 2: Convet the te to yely te. Both methods will wok! Method 1: Thee e 12 months in ye. So in 2 yes thee e 24 months. So P = $0 = 10% pe month Now use the fomul to find simple inteest T = 24 months I = P# # T = $ 0 # 10 # 24 = $ 2400 Method 2: Thee e 12 months in ye. So if = 10% pe month, the yely inteest te is 10% # 12 = 120% So P = $0 = 120% pe ye T = 2 yes I = P# # T = $ 0 # 120 # 2 = $ 2400 Both methods find the sme nswe. So use whiheve method you think is esie. But ememe the time peiods nd the te must mth. Alwys ssume tht 1 ye is lso: unless the question speifies othewise. 12 months o 52 weeks o 365 dys % Inteest Mthletis % 3P Lening SERIES TOPIC 3

6 Bsis Hde Questions with the Simple Inteest Fomul Sometimes the inteest fomul is used to find the vlue of P, R, o T. A etin pinipl mount ened $2310 in inteest t te of 11% p ove 7 yes. Wht ws the pinipl mount? I = $2310 = 11% p T = 7 yes Wite the fomul nd sustitute in the given vlues I = P# # T $ 2310 = P # 11 # 7 Now, solve fo P ` P # 077. = $ 2310 ` P = $ = $ 3000 So the pinipl mount (the initil mount) is $3000. When finding the inteest te, ememe tht it must mth the time peiods. $5700 ws invested ove 36 months nd etuned $8208 in simple inteest. Wht ws the inteest te? P = $5700 I = $8208 T = 36 months Wite the fomul nd sustitute in the given vlues I = P# # T $ 8208 = $ 5700 # # 36 Now, solve fo = $ 8208 $ 5700# 36 ` = 4% Sine the time peiods nd the inteest te must mth, the inteest te must hve the sme time peiods s T... = 4% pe month 4 % Inteest SERIES TOPIC Mthletis % 3P Lening

7 Questions Bsis 1. Find R s deiml if: = 12% p. = 22% p. 2. Find the simple inteest fo the following: P = $1200, R = 0.08, T = 12. P = $2000, = 12%, T = Find the simple inteest fo the following: $4550 t te of 20% p fo 4 yes. $ fo 2 yes t te of 16% p. $ fo 3 months t te of 4.2% pe month. % Inteest Mthletis % 3P Lening SERIES TOPIC 5

8 Questions Bsis 4. Convet the te o the time peiods to ensue they mth. = 3% p, T = 12 months. = 7.8% p, T = 156 weeks. = 9% pe month, T = 2 yes. d = 0.05% pe week, T = 2.08 yes. e = 1% pe dy, T = 1 ye. f = 6% p, T = 1095 dys. 5. You invest $4000 t te of 1.5% pe month fo 3 yes. Find the simple inteest. Wht is the totl mount of money you now own? (ememe: totl mount = pinipl + inteest) 6 % Inteest SERIES TOPIC Mthletis % 3P Lening

9 Questions Bsis 6. A pinipl of $7650 etuns simple inteest of $3672 fte 4 yes. Wht is the inteest te? Convet this inteest te to monthly inteest te. 7. Let's sy you hve $5000 to invest fo 5 yes. Whih of these tes etuns the most inteest? 2.7% pe month. 32% pe ye. 0.7% pe week. % Inteest Mthletis % 3P Lening SERIES TOPIC 7

10 Questions Bsis 8. You fiend Jesse took out lon of $9840 to py fo. Jesse pid k the money y mking $250 pyments eh month fo 4 yes on simple inteest te. Wht is the totl mount Jesse pid k to the nk ove the 4 yes? How muh ext did Jesse py on top of the lon? (Hint: This is the inteest) Wht ws the monthly inteest te used to py off the inteest in? (Hint: P = $9840) d Convet this inteest te to n nnul inteest te. 8 % Inteest SERIES TOPIC Mthletis % 3P Lening

11 Knowing Moe Inteest = Futue Vlue Pinipl Rememe tht the inteest is the 'ext mount' dded to the pinipl fte etin mount of time. The futue vlue of n investment is the totl invested plus the inteest fte etin mount of time. So, if pinipl vlue, (P) ens simple inteest (I ) then the futue vlue (A) is found using this eqution: This mens tht: O Inteest = Finl Amount Pinipl. P + I = A I = A - P A = futue vlue A pinipl mount ens simple inteest of $400 nd the finl mount fte 3 yes is $1200. Wht ws the pinipl? I = A-P ` $ 400 = $ P ` P = $ 800 The finl mount A n lso e found in this wy: A = P+ I I = PRT ` A = P+ PRT ` A = P^1 + RTh R = Suppose you invest $ to en simple inteest t te of 4% pe month fo 1 ye. Find the futue vlue. Step 1: Wite down the vlues we know. P = $ = 4% pe month T = 1 ye Step 2: Mke sue tht the time peiods nd the inteest te mth. The te hs een given pe month nd the time peiods in yes. Let T = 1 ye = 12 months. Step 3: Find R =. R = 4 = 0.04 pemonth Step 4: Use the ove fomul to find the futue vlue. A = P^1 + RTh = $ 12500^ # 12h = $18500 Step 3 in the ove exmple n e skipped if you use this vesion of the fomul: A = P ` 1 + T #. This is lled the simple inteest fomul. Eithe method will wok, so use the one you think is esie. % Inteest Mthletis % 3P Lening SERIES TOPIC 9

12 Knowing Moe Compound Inteest Simple inteest is lled 'flt inteest' euse the inteest dded t the end of eh time peiod is the sme. Compound inteest is diffeent euse the mount of inteest t eh peiod depends on the mount of inteest dded t the pevious time peiod. Think out it like this: Imgine you e investing pinipl P t te of % ompounded t eh time peiod (T). At the end of the 1 st time peiod (eginning of 2 nd time peiod) the futue vlue will e: P `1 + # 1 = P 1 + ` Afte 1 time peiod, T = 1 This vlue eomes the pinipl vlue of the 2 nd time peiod. Let's ll this P 2. At the end of the 2 nd time peiod (eginning of 3 d time peiod) the futue vlue will e: P is the oiginl pinipl vlue P 2 `1 + = P ` + B` + P 1 2 = ` + This vlue eomes the pinipl vlue of the 3 d time peiod. Let's ll this P 3. At the end of the 3 d time peiod (eginning of 4 th time peiod) the futue vlue will e P is the oiginl pinipl vlue P 3 `1 + [ P 1 2 = ] 1 ` + ` + P 1 3 = ` + This vlue eomes the pinipl vlue of the 4 d time peiod. Fom this ptten we n see tht fte n time peiods the futue vlue of the investment, A, is: A P 1 n = ` + Compound inteest fomul This is the fomul to find futue vlue A t ompound inteest te % fo n time peiods. n This fomul ould lso e witten s A = P^1 + Rh. Use the vesion you find esie. R = 10 % Inteest SERIES TOPIC Mthletis % 3P Lening

13 Knowing Moe Hee is n exmple whih uses the ompound inteest fomul. Let's sy you invest $5000 t 4% p ompounded nnully. Wht is the futue vlue fte 7 yes? Using the ompound inteest fomul A P 1 n = ` +. P = $5000 = 4% n = 7 yes ` A = $ 5000`1 + = $ 5000^104. h = $ = $ ( neestent) 7 7 When woking with ompound inteest, the inteest te AND the time peiods need to mth the ompounded te. $ is invested fo 4 yes t te of 15% p ompounded monthly. Find the totl vlue of the investment. Step 1: Convet the nnul inteest te to monthly inteest te (to mth ompounded monthly). Be eful, lthough the inteest te is ompounded monthly, it is still pe ye ('p'). This must e onveted to monthly inteest te to mth the ft tht it is ompounded monthly. Divide the nnul inteest te y 12. = 15% = 1.25% pe month ompounded monthly. 12 Step 2: Mke sue tht the time peiods e in months to mth ompounded monthly. 4 yes = 48 months. So let n = 48. Step 3: Use the ove fomul to find the futue vlue. A P n = `1 + = $ ` 48 = $19700 ^ h 48 = $ ( neestent) % Inteest Mthletis % 3P Lening SERIES TOPIC 11

14 Questions Knowing Moe 1. A pinipl mount of $4500 ens $2 inteest ove time. Wite down the vlues of I nd P. Find the vlue of the finl mount A. 2. $6800 ens simple inteest t te of 3.2% pe month fo 2 yes. Use the simple inteest fomul to find the totl vlue of this investment to the neest ent. Wht ws the inteest ened on this investment to the neest ent? 12 % Inteest SERIES TOPIC Mthletis % 3P Lening

15 Questions Knowing Moe 3. Find the vlue of the totl investment (futue vlue) nd the inteest I fte one ye to the neest ent if: $1200 is invested t te of 5% p ompounded nnully. $ is invested t 12% p ompounded qutely. $ is invested t 8% p ompounded evey 6 months. % Inteest Mthletis % 3P Lening SERIES TOPIC 13

16 Questions Knowing Moe 4. You invest you $375 fo 2 yes. Use the ompound inteest fomul to lulte how muh money you will hve (to the neest ent) if the inteest te is: 7.2% p ompounded nnully. 7.2% p ompounded monthly. 7.2% p ompounded evey 6 months. d Whih is ette investment? 14 % Inteest SERIES TOPIC Mthletis % 3P Lening

17 Using Ou Knowledge Applying Compound Inteest The ompound inteest fomul n e used to find mounts othe thn the totl investment A. It ould e used to find pinipl equied to etun etin totl investment. Hee is n exmple. How muh money do you need to invest to hve $ fte 5 yes if the inteest te is 18% p ompounded monthly? Step 1: Convet the nnul inteest te to monthly inteest te (to mth ompounded monthly). = 18% = 1.5% pe month ompounded monthly 12 Step 2: Mke sue tht the time peiods e in months to mth ompounded monthly. In 5 yes thee e 60 months. So let n = 60. Step 3: Use the ompound inteest fomul to solve fo the pinipl. Rememe, inteest te AND the time peiods need to mth the ompounded te A = P `1 + ` $ 00 = P ` ` $00 = P^1015. h ` P = $00 60 ^1015. h ` P = $ ^neestenth You would need to invest $ to hve $ t the end of 5 yes t this ompounded inteest te. 60 n 60 The ompound inteest fomul n e used to find ny of A, P, o n. Find the nnul inteest te, ompounded nnully equied to hve $ in 4 yes if you invest $6000. Step 1: Mke sue tht the time peiods e in months to mth ompounded monthly. The time peiods (4 yes) is ledy nnul, so no dustment is neessy. Step 2: Use the ompound inteest fomul to solve fo the inteest te. A P n = `1 + $ $ 4 ` 00 = 6000` ` ` = 1 4 ` + = = ^ h ` = ` = 13.62% p ^2 deimlplesh % Inteest Mthletis % 3P Lening SERIES TOPIC 15

18 Using Ou Knowledge Using the Compound Inteest Fomul to Find n Using the ompound inteest fomul to find n (the mount of time peiods) is done y til nd eo. How long will it tke $ invested t 14% p ompounded nnully to gow to n mount gete thn $ 000? Step 1: Use the ompound inteest fomul. A P n = `1 + ` A = $ ` + n = $25000 ^114. h Step 2: Ty diffeent vlues fo n until A is gete then $ : If n = 9yes " thena = $ 25000^114. h = $ Thisislessthn $ : If n = 10 yes " thena = $ 25000^114. h = $ Thisislessthn $ : If n = 11 yes " then A = $ 25000^1. 14h = $ Thisisgete thn $ 000 So it will tke n = 11 yes fo the investment to gow to gete thn $ 000. n Rememe, the inteest te nd the time peiod oth need to mth the ompounded te. Hee is n exmple. Let's sy you hve $2 to invest t te of 12% p ompounded monthly. How long would it tke to hve totl investment etween $3000 nd $3010? Step 1: Convet the nnul inteest te to monthly inteest te (to mth ompounded monthly). = 12% = 1% pe month ompounded monthly 12 Step 2: Use the ompound inteest fomul. A P n = `1 + ` A = $ ` + n = $ 2^101. h n Rememe, inteest te AND the time peiods need to mth the ompounded te Step 3: Ty diffeent vlues fo n until A is etween $3000 nd $ : If n = 34 months " then A = $ 2^1. 01h = $ This is less thn $ : If n = 35 months " then A = $ 2^101. h = $ This is less thn $ : If n = 36 months " then A = $ 2^1. 01h = $ This is etween $ 3000 nd $ : If n = 37 months " then A = $ 2^1. 01h = $ This is less thn $ 3010 So fo the totl investment to e etween $3000 nd $3010, the pinipl of $2 must e invested fo 36 months (3 yes). 16 % Inteest SERIES TOPIC Mthletis % 3P Lening

19 Questions Using Ou Knowledge 1. How muh money do you need to invest if you'e iming to hve $ fte 5 yes nd: the inteest te is 2.4% p ompounded nnully? the inteest te is 2.4% p ompounded monthly? Rememe, inteest te AND the time peiods need to mth the ompounded te % Inteest Mthletis % 3P Lening SERIES TOPIC 17

20 Questions Using Ou Knowledge 2. To hve $5000 in 7 yes fte investing $2360, lulte the equied nnul inteest te (to 2 deiml ples) if the te is: Compounded nnully. Compounded monthly. Rememe, inteest te AND the time peiods need to mth the ompounded te 18 % Inteest SERIES TOPIC Mthletis % 3P Lening

21 Questions Using Ou Knowledge 3. A pinipl investment P is invested fo 10 yes. Answe these questions oet to 2 deiml ples. Use the simple inteest fomul to find the simple inteest te equied fo the investment to doule. (Hint: A = 2P) Use the ompound inteest fomul to find the inteest te ompounded nnully equied fo it to doule the pinipl. % Inteest Mthletis % 3P Lening SERIES TOPIC 19

22 Questions Using Ou Knowledge 4. How long will it tke to en totl investment gete thn $ if you invest $ t inteest te of: 18% p ompounded nnully? 18% p ompounded monthly? 18% p ompounded qutely (4 times ye)? d Whih is quike? 20 % Inteest SERIES TOPIC Mthletis % 3P Lening

23 Thinking Moe Lons Bnks nd othe ognistions whih lend money lwys hge inteest on thei lon. The lon is lwys the pinipl (P) nd the oowe will hve to py the lon k nd py inteest in ddition. Dyln took out lon of $7200 fom nk to help py fo. Dyln is equied to py the lon off ove the next 3 yes t n inteest te of 8% p ompounded qutely. Wht is the totl mount tht Dyln will py fo the lon? Step 1: Convet the nnul inteest te to qutely inteest te (to mth ompounded qutely). Compounded qutely mens evey 3 months (4 times eh ye). So, divide the nnul inteest te y 4. = 8% = 2% pe qute ompounded qutely 4 Step 2: Mke sue tht the time peiods e in qutes to mth ompounded qutely. 3# 4qutes = 12 qutes. So let n = 12. Step 3: Use the ompound inteest fomul to find the futue vlue. A P n = ` = $ ` + 12 = $ 7200^102. h = $ ( neestent) So Dyln is tully equied to py the ognistion tht lent him money moe thn the lon. This is how nks nd money lending ognistions mke pofit. To find the nk's pofit, ust find the inteest using the fomul I = A - P I = $ $7200 = $ Often the oowe hs to py k the totl mount in equl pyments. These e usully eh month o eh week. Hee is wht hppens in the se of the exmple ove. Dyln must py the lon off in equl monthly pyments. Wht is the vlue of eh monthly pyment? Totlmount pid Monthlypyments = Months in 3 yes = $ = $ ^neestenth This mens Dyln will py $ eh month fo the next 3 yes to py off the lon. % Inteest Mthletis % 3P Lening SERIES TOPIC 21

24 Thinking Moe Conveting Reduile Inteest to Flt Inteest Sometimes money lende mkes the oowe py off lon using 'eduile inteest'. This is diffeent to simple nd ompound inteest euse the inteest hged edues s the mount owing deeses. Reduile inteest is moe omplited to wok with, so it is impotnt to e le to onvet eduile inteest to simple inteest. The good news is tht thee is tle whih onvets eduile inteest to simple inteest (flt inteest). It onvets nnul o monthly eduile inteest tes to nnul flt tes. This tle is on the lst pge of this ook. Convet the following eduile inteest tes into equivlent flt inteest tes using the eduile inteest tle Reduile te of 9% p ove 2 yes Equivlent flt te is 4.82% pe ye Reduile te of 5% p ove 4 yes Equivlent flt te is 2.64% pe ye Reduile te of 1% pe month ove 5 yes This is eduile te of 12% p ove 5 yes Equivlent flt te is 6.69% pe ye d Reduile te of 1.25% pe month ove 10 yes This is eduile te of 15% p ove 10 yes Equivlent flt te is 9.36% pe ye Hee is n exmple how to use this tle in lultions. You e equied to py off lon of $4000 t eduile inteest te of 15% p ove 6 yes Find the equivlent simple inteest te fom the tle This eduile inteest te is equivlent to flt te of 8.71% Use the flt te to lulte the totl mount you will py k fte 6 yes. This is flt te so the simple inteest fomul is used A = P `1 + # T = $ ` + # 6 = $ 4000^ h = $ Wht is the inteest on you lon? I = A-P = $ $4000 = $ % Inteest SERIES TOPIC Mthletis % 3P Lening

25 Questions Thinking Moe 1. Use the tle onveting nnul eduile inteest tes to equivlent nnul flt tes to nswe these questions. Convet the 7% p eduile inteest te ove 6 yes to flt te. Wht is the equivlent nnul flt inteest te to 9% p eduile inteest ove 3 yes? Wht is the equivlent nnul flt inteest te to 15% p eduile inteest ove 8 yes? d Wht is the equivlent nnul flt inteest te to 1.25% pe month eduile inteest ove 5 yes? e Wht is the equivlent nnul flt inteest te to 0.75% pe month eduile inteest ove 9 yes? 2. If to py lon off, you e equied to py totl mount of $ ove 6 yes, then: If you pln to py yely, wht is you nnul epyment? If you pln to py monthly, wht is you monthly epyment? If you pln to py weekly, wht is you weekly epyment? % Inteest Mthletis % 3P Lening SERIES TOPIC 23

26 Questions Thinking Moe 3. A nk lons Gy $ He must py the lon off ove the next 8 yes with inteest hged t te of 11% p ompounded nnully. Do the time peiods mth the te the inteest is ompounded? Does the inteest te mth the the te the inteest is ompounded? Find the totl mount Gy will hve pid fte he hs pid off his lon. d If Gy is equied to py this lon off monthly, how muh will he hve to py eh month? e If Gy is equied to py this lon off qutely, how muh will he hve to py eh qute? 24 % Inteest SERIES TOPIC Mthletis % 3P Lening

27 Questions Thinking Moe 4. Let's sy you oow $ 000 fom nk to put deposit on house. The nk hges you inteest t 16.8% p ompounded monthly fo the next 8 yes. Convet the nnul inteest te ompounded monthly to monthly te ompounded monthly. Why is this neessy? Find the totl mount you will hve pid to the nk fte 8 yes. How muh pofit did the nk mke? d Wht is the vlue of eh monthly pyment? % Inteest Mthletis % 3P Lening SERIES TOPIC 25

28 Questions Thinking Moe 5. Ashley tkes out lon of $3600. She is equied to py the lon k ove 3 yes t eduile inteest te of 9% p. Find the equivlent nnul flt inteest te fom the tle. Use the flt inteest te to find the totl Ashley will hve pid ove the 3 yes in pying off he lon. If Ashley is equied to mke qutely pyments, then how muh must she py eh qute? d If Ashley is equied to mke monthly pyments, then how muh is Ashley equied to py eh month? 26 % Inteest SERIES TOPIC Mthletis % 3P Lening

29 Questions Thinking Moe 6. Find you monthly pyments if you tke out lon of $8500 t eduile inteest te of 11% p ove 10 yes. % Inteest Mthletis % 3P Lening SERIES TOPIC 27

30 Thinking Moe Tle to onvet eduile inteest tes to equivlent flt tes Annul Reduile te (% ) Annul Reduile te s deiml R ` = Monthly Reduile te s deiml ` 12 Equivlent nnul flt te (%) pe ye (ounded to 2 d.p.) % 1.58% 1.56% 1.56% 1.56% 1.57% 1.57% 1.58% 1.58% 1.59% % 2.11% 2.10% 2.09% 2.10% 2.11% 2.12% 2.13% 2.14% 2.15% % 2.65% 2.63% 2.64% 2.65% 2.66% 2.67% 2.69% 2.71% 2.73% % 3.18% 3.17% 3.18% 3.20% 3.22% 3.24% 3.27% 3.30% 3.32% % 3.73% 3.72% 3.74% 3.76% 3.79% 3.83% 3.86% 3.90% 3.93% % 4.27% 4.27% 4.30% 4.33% 4.37% 4.42% 4.46% 4.51% 4.56% % 4.82% 4.83% 4.86% 4.91% 4.96% 5.02% 5.08% 5.14% 5.20% % 5.37% 5.39% 5.44% 5.50% 5.56% 5.64% 5.71% 5.78% 5.86% % 5.93% 5.95% 6.01% 6.09% 6.17% 6.26% 6.35% 6.44% 6.53% % 6.49% 6.52% 6.60% 6.69% 6.79% 6.90% 7.00% 7.11% 7.22% % 8.18% 8.27% 8.40% 8.55% 8.71% 8.87% 9.03% 9.20% 9.36% % 9.91% 10.05% 10.25% 10.47% 10.70% 10.94% 11.17% 11.40% 11.62% % 11.07% 11.26% 11.52% 11.79% 12.08% 12.36% 12.64% 12.92% 13.19% 28 % Inteest SERIES TOPIC Mthletis % 3P Lening

31 Answes Bsis: Knowing Moe: 1. R = 0.12 R = I = $2 2. I = $1152 I = $1920 P = $4500 Finl mount = $ I = $3640 I = $6300 I = $ A = $ I = $ T = 1 ye OR T = 3 yes OR = 0.25% pe month = 0.15% pe week 3. A = $1260 I = $60 T = 24 months OR = 108% p A = $ d T = weeks OR = 2.6% p I = $2096 e T = 365 dys OR = 365% p A = $ f T = 3 yes OR = 0.016% pe dy I = $ I = $2160 Totl money now own is $ A = $ A = $ A = $ = 12% p = 1% pe month d 7.2% p ompounded monthly is ette investment sine thee is highe etun % pe week gives the highest te of etun pe nnum, it will e the te tht etuns the most inteest. 1. Using Ou Knowledge: P = $ P = $ Totl mount pid = $ Ext pid = $2160 = 0.46% pe month 2. = 11.32% p = 10.77% p d = 5.5% p 3. = 10.00% p = 7.18% p (to 2 d.p.) ompounded nnully % Inteest Mthletis % 3P Lening SERIES TOPIC 29

32 Answes Using Ou Knowledge: Thinking Moe: 4. It will tke 8 yes fo the investment to e gete thn $ It will tke 85 months to en moe thn $ It will tke yes to en moe thn $ % pe month This is neessy sine the fomuls only wok when units e onsistent. Fo exmple, sine the inteest te is ompounded monthly it wouldn t mke sense to use yes s you time peiod sine the inteest te is not ompounded nnully. d It would e quike to invest in n inteest te tht is ompounded monthly in ode to eh the $ fste. A = $ I = $ Thinking Moe: d Eh pyment = $ % p 4.83% p % p 9.03% p d 8.55% p Totl = $ e 5.14% p $ pe qute 2. $1872 p $156 pe month d $ pe month $36 pe week 6. $ pe month 3. d e Yes, sine the inteest te is ompounded nnully nd the time peiod speifies ye figue the time peiod nd the peiod the inteest te is ompounded do mth. Yes, the inteest te is pe nnum figue nd the inteest te is ompounded nnully then the inteest tes mth up. A = $ $ pe month $ pe qute 30 % Inteest SERIES TOPIC Mthletis % 3P Lening

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34 Inteest