FROM THE ANSWER SERIES

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1 FINNCIL MTHS QUESTIONS & NSWERS 1 FROM THE NSWER SERIES publshed by : The nswer 210 Man Road CLREMONT 7708 Cape Town tel: (021) fa: (021) e-mal: nfo@theanswerseres.co.za

2 QUESTIONS

3 ESSENTIL FOR FINNCIL MTHS!!! Geometrc seres : The Theory of nnutes Questons 1. Use the formula for the sum of a geometrc seres to determne : (1 + ) + (1 + ) (1 + ) n - 1 (where 1 + > 1) Now, see f you can WRITE DOWN a formula for the followng : (1 + ) + (1 + ) (1 + ) n Compare 1.2 to What s the same? What s dfferent? Then notce n the answer : What s the same? What s dfferent? 1.3 (1 + ) + (1 + ) 2 + (1 + ) (1 + ) n nswers 1.1 S n? ; a ; r 1 + ; n n... note : there are n terms! S n â S n ( ) n n ( 1+ ) Sn n a(r - 1) r-1 ; r > gan : a & r 1 +, BUT, number of terms n + 1! So, S n + 1? â S n + 1 n+1 ( 1+ ) Now, a (1 + ) ; r stll 1 + & no. of terms n ; S n? â S n ( 1+) ( ) n a p -1 ; r p -1 & number of terms n ; S n? FINNCIL MTHS NB: Be sure to see pplcatons (Fnancal Maths) - Patterns and Sequences - for several eamples on compound ncrease and decrease and, partcularly, the use of TIMELINES - they make fnancal maths so easy!!! SIMPLE ND COMPOUND INCRESE ND DECRESE 1.1 Calculate the value of an nvestment of R that earns smple nterest of: (a) 9,8% p.a. over 5 years. (b) 6,75% p.a. over 6 months. 1.2 How much nterest wll be pad n each case? 2. I want to sell my caravan. The current value of ths caravan s R Calculate ts orgnal value f I bought t 5 years ago and the value deprecates on the straght lne method (a flat rate ) of 9% per year. 1 Q FINNCIL MTHS 2. Now, determne : 2.1 p + p p n p.e. p -1 + p -2 + p p -n 2.2 and n the same way as 2.1 : 1+.e. + (1+ ) 2 + (1+ ) 3 1 where < 1 p n (1+ ) - 1 (1 + ) + (1 + ) (1 + ) (1 + ) - n 2.2 s qute a bt dfferent to , but dentcal to has replaced p. (where (1 + ) -1 < 1) S n -1 -n p ( 1 - p ) p 1-p-1 p -1 -n. p. p (1 - p ) -1 p - p. p -n (1 - p ) p-1 %... Sn.... a(1 - r n) 1-r What you need to know s that : p -1 % p 1 p % p 1! ; r < 1 We may multply a fracton, top & bottom, by the same number. 2.2 a (1 + ) - 1 ; r (1 + ) - 1 & number of terms n ; Sn? S n -1-1 n 1 - (1+ )-1 ( 1+ ) 1 - ( 1+ ) ( ) -n ( ) n (1+ ) % (1+ ) Compare ths workng to has replaced p! 3.1 Calculate the value of an nvestment of R that earns compound nterest of 9,8% p.a. over 5 years. 3.2 How much nterest wll be pad n ths case?. partcular car was bought for R What wll the book value of the car be after 5 years f the rate of deprecaton s 16% p.a. where deprecaton s based on:.1 the straght lne method (.e. smple nterest).2 the reducng-balance method (.e. compound nterest) 5. You wn R n the LOTTO and want to nvest the money wsely for the net fve years. The followng optons are avalable: BNK offers 11,1% nterest p.a., compounded quarterly. BNK B offers 10,8% nterest p.a., compounded monthly. Show the calculatons needed to decde whch s the best opton. 6. Bongan and Barry each have R Barry nvests hs money for 5 years at 10% p.a. compounded monthly. Bongan nvests hs R1 500 for 5 years at 10% p.a. compounded half-yearly. What s the dfference n ther accrued amounts at the end of the 5-year perod? 1.15 Copyrght The nswer TOPICS QUESTIONS

4 Q TOPICS QUESTIONS FINNCIL MTHS 7.1 Calculate each of the followng and wrte down whch s a better nvestment. : n amount s nvested at a smple nterest rate of % per annum for 8 years. B: n amount s nvested at a compound nterest rate of 10% per annum for 8 years. 7.2 What compound nterest rate would yeld the same amount as nvestment? (Correct to decmal dgts.) 8. fnancal consultant ndcates that he can treble the value of an nvestment at the end of 6 years. If the nterest rate s fed and compounded monthly, calculate the annual rate of nterest that he offers. 9. The annual rate of deprecaton of a certan knd of machne s 15%, based on the reducng balance method. When new, the prce s R fter how many years wll one of these machnes be worth R10 000? (Correct to 2 decmal dgts). 10. In January 2008, a Metro communty centre receved R towards the buldng of a new swmmng pool. The money was nvested at 13,25% compounded annually. When the nvestment grows to one mllon rand, the centre wll commence the project. In whch year wll ths be? 11.1 Complete the followng table for an nvestment at 18% p.a. compounded: annually sem-annually quarterly monthly Interest rate per tme perod Factor of ncrease 1 + Quoted tme â Number of tme perods 5 yrs 10 yrs n n 1 yr n 20 yrs n 18% , If P Rand s nvested n each of the four cases above, wrte, n terms of P, the value of the nvestment: FTER: (1 + ) 1 year 5 years 10 years 20 years (1,18) (1,09) (1,05) (1,015) NOMINL ND EFFECTIVE INTEREST RTES 1. Complete the followng table for an nvestment of P Rand at 18% p.a. compounded: annually sem-annually quarterly monthly Nomnal annual nterest rate Copyrght The nswer Value after 1 YER ncrease factor Effectve annual nterest rate (m) 1 + eff eff 1,18 P(1,18) 18% 1,18 1,09 P( ) 2 18% 1,05 18% 1,015 18% 2.1 fter 1 year, compare the nomnal and effectve nterest rates when compoundng s annual. 2.2 Does the effectve nterest rate ncrease or decrease as the number of compoundng perods per year ncreases? 2.3 Calculate the effectve nterest rate f the nterest was compounded daly. 3. Calculate the effectve yearly rate (correct to one decmal place) f an nvestment offers a nomnal rate of 13,5% p.a., compounded : 3.1 quarterly. 3.2 monthly. 3.3 daly.. Calculate the nomnal nterest rate f the effectve nterest rate s :.1 15%, whle nterest s compounded quarterly..2 13,5%, whle nterest s compounded monthly. 5. Emma s nvestment grows from R7 000 to R9 30,60 n a perod of three years. Interest s compounded quarterly. Calculate: 5.1 the nomnal nterest rate on her nvestment. 5.2 the effectve nterest rate on her nvestment. TIME LINES 1. Lndwe nvested R5 000 at 10% per annum compounded semannually (every s months). fter 2 years the nterest rate changed to % per annum compounded monthly. Fnd the value of the nvestment after 5 years. 2. certan bank offers nterest at 10% per annum compounded monthly for the frst three years and 15% per annum compounded monthly for the followng four years. What lump sum must be nvested now n order that R can be wthdrawn n 7 years tme? 3. Mrs I Plan wll need R6 260 at the end of ten years. She makes two deposts n order to save ths money: Rand at the end of 2 years R3 000 at the end of 8 years (6 years after the frst depost) Interest s calculated at 10% p.a. compounded annually for the frst years and then at % p.a. compounded quarterly thereafter. Calculate the value of f the accumulated amount s eactly the amount she needs.. Schalk borrows R5 from Stormers Bank. He undertakes to repay the loan as follows : R3 000 one year from now R1 000 four years from now R s years from now R 000 ten years from now, whch wll then redeem the loan. Calculate f the compound nterest for the frst 5 years s calculated at % p.a. and for the last 5 years nterest s calculated at 10% p.a. compounded b-annually. 5. Mr Maharaj has two chldren aged 11 and 15 years who share the same brthday. On ther brthday he nvested a total of R n two separate accounts, so that each would receve the same amount on ther 21 st brthdays. He opens accounts that earn nterest at % per annum compounded monthly. How much money dd Mr Maharaj nvest n each account? We assume that the money was nvested on the 11 th and 15 th brthday.

5 6. father has 3 chldren whose present ages are, 15 and 17 years. He plans to gve them R0 000 each on ther 21 st brthday. How much money must he nvest now f the nterest rate s 1% per annum compounded monthly? SINKING FUNDS SINKING FUND s establshed to afford replacng an tem/ equpment, etc, at some future date. It s the DIFFERENCE - at a future date - between : the antcpated cost of the new tem, and the re-sale value of the old tem at that tme. Regular, equal payments (called annutes) are an deal way to save towards a snkng fund. There wll be eamples of ths n the net secton (nnutes). 1. contractor buys a truck for R The value of the truck deprecates by 30% per annum on a reducng balance. Ths truck wll need to be replaced at the end of years. The value of a new truck s epected to apprecate by 18% per annum. 1.1 Calculate the resale value of the truck n years tme. 1.2 What should be the value of a snkng fund that needs to be set up to pay for the new truck, f the old truck s used as a trade-n? 2. mllng machne presently costs R The value of the machne deprecates at 20% p.a. on the reducng balance. new machne wll be needed n 10 years. The cost of the new machne wll grow by 10% p.a. Calculate: 2.1 the scrap value of the frst machne; 2.2 the cost of the replacement machne; and 2.3 the value the snkng fund must attan to purchase the second machne. 3. Jonathan buys a car for R wth the ntenton of replacng t wth a smlar one n 5 years tme. The value of the car deprecates at 22% per annum on a reducng balance whle the prce of a smlar car s epected to ncrease by 19% each year. 3.1 Calculate the resale value of Jonathan s car n 5 years tme. 3.2 What should be the value of a snkng fund that needs to be set up to pay for the new car f the old car s used as a trade-n? NNUITIES NB: It s essental to do the Theory of nnutes on Page 1.15, at the end of the Patterns and Sequences topc to understand the formulae for future and present value annutes. INVESTMENTS / SVINGS / RETIREMENT 1. Theresa deposts R600 at the end of each month nto a savngs account payng 1% nterest p.a. compounded monthly. Calculate the amount n her account 18 months after the frst depost was made. 2. On my s 10 th brthday her father decdes to start nvestng a fed amount for her every month, tll she reaches her 18 th brthday. He wants t to grow to R Calculate the monthly nstalments f the nterest rate s 11,% p.a. compounded monthly. 3. parent wants to provde for her daughter Mary to be able to buy a car when she turns 18, by payng a fed amount each month nto a savngs account, bearng nterest of % per annum compounded monthly. Mary has just turned 8. Her mother estmates that Mary wll need R when she turns Calculate how much she wll have to pay nto the savngs account each month, wth the frst payment beng n a month s tme. 3.2 Calculate how much there wll be n the account after 7 years.. Susan s mother buys a car for R It s epected to deprecate at the rate of 20% p.a. Susan agrees to buy the car from her mother at the deprecated value at the end of fve years..1 What wll the car be worth at the end of fve years usng the reducng balance method of deprecaton?.2 If the nterest s calculated at 10% p.a. compounded monthly, what equal amounts must Susan nvest each month f she s to have suffcent funds n the bank at the end of the fve years to purchase a car? 5. Thandle plans to retre n 10 years tme. He has calculated that he needs an amount equvalent to the buyng power of R of today s rands. He epects nflaton to be,5% per annum for each of the 10 years. 5.1 What amount does he need to have n hs account n 10 years tme? 5.2 He plans to make equal monthly payments for the net 10 years, startng n a month s tme, nto an account payng 9,9% nterest per annum compounded monthly. How much are hs monthly payments? LONS 1. loan of R s repad over 20 years by means of equal monthly nstalments, startng one month after the loan was granted. The nterest rate s 15% p.a. compounded monthly. 1.1 What s the future value of the loan,.e. ts accrued value over 20 years? 1.2 If the monthly payments are rand, determne an epresson n for the (sum of the) future values of the payments by the end of the 20 years. 1.3 Calculate the monthly repayment. 1. Confrm your answer to 1.3 by makng use of the present value annuty formula. 2. Mr Ndlovu has taken out a mortgage bond of R to help pay for hs house. The bond s repayable n equal monthly nstalments over 25 years at a rate of 18,75% per annum, compounded monthly. 2.1 Calculate hs monthly payment. 2.2 Calculate the balance outstandng after 16 years. 3. Sunshne Cars agrees to sell Ray a car on a no-depost plan provded he pays the amount owng n 10 months. The nterest rate s 18% per annum and s charged at the end of each month. Ray works out that f he pays R6 300, at the end of each month, hs debt wll be cleared n 10 months. 3.1 Calculate the cash prce of the car. 3.2 Calculate the effectve annual nterest rate that Ray wll pay Copyrght The nswer 1 Q TOPICS QUESTIONS FINNCIL MTHS

6 Q TOPICS QUESTIONS FINNCIL MTHS. loan of R s repad n monthly nstalments over,5 years. If nterest s at 18% p.a. compounded monthly, calculate:.1 the payment for each month..2 the balance outstandng after payments. SINKING FUNDS (nvolvng nnutes) 1. Mr Bauer s a farmer needng new farm equpment. He buys a brand-new tractor costng R It s epected to have a useful lfe of 8 years. He accordngly sets up a snkng fund to enable hm to buy a new tractor wthout havng to use credt facltes n 8 years tme. He decdes that he wll not sell ths tractor n 8 years tme when he buys a new one. 1.1 What s the predcted nflaton rate f a new tractor s epected to cost R07 565,51 n 8 years tme? 1.2 What equal monthly payments (96 of them, startng at the end of the frst month) must be pad nto the fund, at an nterest rate of % p.a., n order for the fund to reach the necessary value of R07 565,51? 2. Top Class Prnters bought a prntng machne for R They epect to replace ths machne wth a new one n 6 years' tme. The rate of deprecaton s 20% per annum on the reducng balance whlst the cost of a new machne escalates by 15% per annum. 2.1 What s the scrap value of ths machne n s years tme? 2.2 What wll t cost Top Class Prnters to replace ths machne f the old machne s traded n? 2.3 Top Class Prnters sets up a snkng fund to cover the replacement cost of ths machne. Payments are made nto a bankng account payng nterest at 18% per annum compounded monthly. Fnd the value of the monthly payments f payment commences at the begnnng of the month n whch the machne was bought and ends at the begnnng of the last month. 3.1 What s the total amount (correct to the nearest R1 000) that the snkng fund must accrue to? (.e. the dfference between the antcpated cost of the new equpment and the re-sale value of the old equpment). If the company s offered an nterest rate of % p.a. compounded monthly, calculate: 3.2 how much the equal monthly payments nto the snkng fund wll be. ssume that money s deposted at the begnnng of each month, startng mmedately, and at the end of the last month before the new equpment s purchased. HIRE PURCHSE 1. Dashng Dan has a choce of two dfferent ways of fnancng the purchase of a new car: he can get a bank loan, to be pad over four years, n 8 equal monthly nstalments, startng n one month s tme, or he can get a hre purchase agreement, also to be pad off n 8 equal nstalments, startng n a month s tme. The bank loan wll charge 19,5% p.a., compounded monthly on the reducng balance. The hre purchase company wll charge % p.a., smple nterest, on the full amount borrowed for the four year perod. If Dan needs to borrow R : 1.1 What wll the amount of hs monthly payments be f he takes the bank loan opton? 1.2 What s the greatest value of r, (the smple nterest rate), whch wll stll make the hre purchase opton better for Dan? 2. motorcycle costs R Smon Student pays a 25% depost and wll pay the balance over a perod of two years, n equal monthly payments. Fnd the sze of the monthly payments f : 2.1 Smon borrows the balance at 20,7% p.a., compounded monthly. 2.2 Smon borrows the balance on hre purchase, where the smple nterest s 13% per annum. 3. small company plans to replace ts operatng equpment n 5 years tme. The present value of ths equpment s R To guard aganst nflaton, they plan to mplement a snkng fund whch wll take prce ncreases related to a 9% p.a. nflaton rate nto account. They estmate that they wll be able to sell off ther old equpment for R Copyrght The nswer 1.18 MONEY LENDERS 1. money lender grants a loan of R to Sandy at 2% per annum compounded monthly. Sandy agrees to pay the loan over a perod of one year. She pays R6 000 after 3 months, R5 000 after 6 months and R8 500 four months later. Calculate the amount of Sandy s fnal payment at the end of the year. 2. Nomonde needs to borrow money to vst her ll mother. She borrows R00 from a mcrolender and agrees to pay back R900 one month later. 2.1 What s the monthly nterest rate? 2.2 Determne the effectve annual percentage rate of compound nterest that the mcrolender charged her. PYRMID SCHEMES 1. pyramd scheme promses nvestors that ther money wll grow at 15% per week. What s the effectve annual percentage rate of growth promsed?

7 NSWERS

8 M Copyrght The nswer M1.28 TOPICS NSWERS FINNCIL MTHS

9 2.1 They are the same. 2.2 It ncreases % 365 0, â 1 + 1, â Value of nvestment (P) after one year P(1,000 93) 365 P(1, ) â P s ncreased by a factor of 1, â Effectve rate s 0, j 19,72% 1 + n F v 13,5% 13,5% 13,5% 365 The ncrease factor Effectve annual nterest rate 1,03375 P(1,0375) 1, ,2% 1,015 P(1,015) 1, ,% 1, P(1,000369) 365 1, ,5% OR : Use the formula : Be sure to understand ths 1 + eff (m) m though - maybe by workng m through the tables above. where eff s the effectve nterest rate ,15 â 1 + (m) (m) s the nomnal nterest rate & m s the number of compoundng perods n 1 year. (m) 1+ 1,15 1, (m) â 0, â (m) 0, ,2% 5. P v ; F v 9 30,60 ; n 3 % 5.1 (m) P v 1+ (m) 1+ â 1 + (m) â â (m) F v 1, ,02 0,02 â (m) 0,096 9,60% ,135 (m) 1+ (m) 1,135 â 1 + 1, (m) â 0, â (m) 0,73...,7% eff 9,6% 1+ 1,0995 â eff 0,0995 9,95% % 0,05 â 1 + 1,05 TIMELINES T 0 2 years T 2 3 years T 5 ( half-years) (36 months) R (1,05) â fter 5 years, F v 5000(1,05). (1,01) 36 10% 0,0083 â 1 + 1,0083 (STOre n ) â P. 36. B â P v 36 B8 j R8695,5. j R61 288,82 % 0,01 â 1 + 1, B (1,05). (1,01) 36 T 0 3 years T years 3 T 7 (36 months) (8 months) P v? R P P % 0,05 â 1 + 1,05 (STOre n B) P. 36. B % 0,01 % 0,03 â 1 + 1,1 â 1 + 1,03 F v R6 260 T 0 T 2 T T 8 T 10 2 years (1,1) 2 rand (6 yrs) 2 quarter-years (1,1) 2.(1,03) (1,03) 8 The accumulated amount : (1,1) 2 (1,03) (1,03) â B B â R1 000,00. T 0 T 1 T T 5 T 6 T years 3 000(1,) 5. (1,05) 8 R (1,) (1,05) (1,).(1,05) 10 + (1,05) (1,) 5 (1,05) 10 â + B +.C D â + B D - C (5D - C) + B â 5D - C â R1 09,53 It would have been better to have used present values - try! T 0 T 6 T yr old R % 0, â 1 + 1, P v 5 R years / 72 months 15 yr old R( ) F 11 F 15 â. ( ).B B -.B â. +.B B â ( + B) B B â + B R11 8,6 10% 0,05 2 â 1 + 1,05 (5)(1,) 5 F v 5 (1,) 5 (1,05) (1,) 1 5 yrs (10 half-yrs) yrs (8 half-yrs) % 0,01 â 1 + 1,01 10 years / 0 months â He nvests R11 8,6 for the 11 year old & R18 515,5 for the 15 year old 3 000(1,) (1,05) (1,) 1 (1,05) 10 F 11 (1,01) 0. F 15 ( )(1,01) 72 ( ).B M1.29 Copyrght The nswer 1 M TOPICS NSWERS FINNCIL MTHS

10 M FINNCIL MTHS 6. We wll use the PRESENT VLUE FORMUL : 1% 0,0116 â 1 + 1,0116 STOre n T 0 T T 6 T 9 P years / 108 months yr old R0 000 P yr old P yr old mount to nvest NOW P 1 + P 2 + P ( ) j R51 70,35 6 years / 72 months years / 8 months R0 000 SINKING FUNDS 1.1 F v P v(1 - ) n (1-0,3) R New truck P v(1 + ) n (1 + 0,18) R ,66 â Snkng fund should be : R , R , Scrap value P v(1 - ) n (1-0,2) 10 R32 2,25 (STOre n ) 2.2 Cost of new machne P v(1 + ) n (1 + 0,1) Snkng fund B - R75 910,9 R0 000 R778 2,7 (STOre n B) NNUITIES INVESTMENTS / SVINGS / RETIREMENT 1% 0,0116 (STOre n ) â 1 + 1,0116 (STOre n B) R600 R600 R600 R600 R600 T 0 T 18 ( 1+) n -1 F v j R11 90, ( B -1 ) Do the theory of nnutes eamples on p1.15 to understand the formula OR : Set up a geometrc seres, startng wth the LST depost : F v B B B 17 (18 terms) 600 ( B 18-1 ) a(rn - 1)... S n B -1 r-1 11,% 0,0095 (STOre n ) â 1 + 1,0095 (STOre n B) F v T 0 (8 years) T months F v of the payments ( 1+) n -1 j.c ( B 96-1) â.c â C j R62, fter 7 years,.e. 8 months ( 1+) ,2 1,01-1 Value 0,01 R51, % 0,2 ; P v ; n 5 F v P v(1 - ) n (0,8) 5 R26 21,0.2 10% 0,0083 (STOre n ) â 1 + 1,0083 (STOre n B) T 0 (5 years) T months F v ( 1+) n -1 ( B 60-1).C Now,.C R26 21, â R338,53 T 0 10 years T 10 P v F v (1,05) 10 F v of payments,5% 0,05 â 1 + 1,05 9,9% 0,00825 â 1 + 1,00825 B ( B 0-1).C D j R ,2 D T 0 (10 years) T 0 0 months TOPICS NSWERS 3.1 F v of old car (1-0,22) 5 R3 307,62 (STOre n ) 3.2 F v of smlar new car (1 + 0,19) 5 R ,09 (STOre n B) â Snkng fund B - R31 65, â R391,2 Copyrght The nswer M % 0,01 (No need to store!) â 1 + 1,01 F v T 0 (10 years) T 0 0 months F v of payments ( 1,01) 0-1 0,01. â D C j R7 62,71 Unfortunately, the Present value formula can t be used here as t won t cater for nflaton.

11 .1 F v P v (1 + ) n where LONS P v R ; 15% 0,05 ; n 20 % 20 â 1 + 1,05 - the ncrease factor â F v (1,05) 20 j R ,35 STOre n P v R F v The nstalments years T 0 T 1 T 2 (20 months) T 239 T 20 â F v (of the nstalments), startng wth the last one : + (1 + ) + (1 + ) (1 + ) (1 + ) â F v 20 (1 + ) ,05-1 0,05... S n terms n a(r - 1) r-1 [.B] STOre n B (R1 97, ) 1.3 â.b â B j R1 316,79 1. THE PRESENT VLUE METHOD (1 + ) - 1 (1 + ) - 2 (1 + ) (1 + ) - 20 P v of the loan R (1 + ) (1 + ) 238 (1 + ) 239 T 1 T 2 T 239 T P v of the nstalments (1 + ) (1 + ) (1 + ) (1 + ) terms -1-1 { } 20 (1 + ) 1 - (1 + ) (1+ ) % 1-(1+) -1 (1+ ) (1+) ,0,5 0,05.C STOre n C (R75,92... ) â.c P v! â R1316,79 Ths confrms the value obtaned n 1.3 (va the FUTURE VLUE METHOD!) Future value of payments : 300 (1 + ) - 1 B D â.d C 2.2 Method 1 : T 0 25 years T 300 (300 months) P v R ,75% 0, (STOre n ) â 1 + 1, (STOre n B) â C D R3 155,13 F v (1 + ) B 300 R ,55 (STOre n C) T 0 16 years 9 years T 300 (192 months) T 192 (108 months) Regard T 192 as the present and T 300 as the future. Calculate the present value of the remanng 108 payments : 3.1 Method 2 : Regard T 0 as the present and T 192 as the future. fter 192 months : Future value of the loan B 192 STOre n C B & Future value of 192 payments... â Balance of the loan C - D R16 085,06 Hs debt the cash prce of the car P v of the 10 payments ,015 0,015 R58 099, eff (1,015) 1,1956 â eff 0, ,56% per annum B PRESENT â Balance of the loan.. VLUE. FORMUL R16 08,77 M1.31 Copyrght The nswer T 1 T 0 T 1 years 2 T 5 R (5 months) P v 18% 0,015 â 1 + 1,015 18% 0,015 â 1 + 1, ,015 0, â â R950,30 FUTURE VLUE FORMUL T 0 T 2 10 months T 10 OR The FUTURE VLUE method.2 Balance outstandng after months Present value of the remanng 2 payments ,30 1-1,015 OR 0,015 The FUTURE R29 53,65 VLUE method 1 M TOPICS NSWERS FINNCIL MTHS

12 M TOPICS NSWERS FINNCIL MTHS 1.1 F v P v(1 + ) n 1.2 SINKING FUNDS (nnutes) , (1 + ) 8 â 1, (1 + ) 8 â , , â 0, â Predcted nflaton rate 6,30% T 0 8 years T 96 (96 months) 96 (1,01) - 1 F v of the payments 0, ,51 â R2 58, 2.1 F v P v(1 - ) n (1-0,2) 6 R (1 + ) (1 + ) (1,015) (1,015) - 1 0, ntcpated cost of the new equpment (1,09) 5 R87 701,56 & The re-sale value of the old equpment R â Snkng fund must accrue to : R87 701,56 - R j R % 0,01 â 1 + 1,01 T 0 T 1 5 years T 59 T 60 (60 months) (1 + ) n+1 (1 + ) - 1 F v... See p1.15 : 61 (1,01) (1,01) - 1 Theory of nnutes Q1.2 & Q1.3 0,01 n combnaton. STOre n â to understand ths formula..d â.d C â C D j ny nterest rate less than 11,20% wll make the hre R7 888,2 purchase a better opton for Dan. Copyrght The nswer M1.32 â j R925, F v P v(1 + ) n (1,15) 6 R ,38 B HIRE PURCHSE â Replacement cost (on trade-n) B - j R , C ,5% 0,01625 Begnnng of the frst month! 18% 0,015 â 1 + 1,01625 B â 1 + 1,015 T 0 T 1 T 2 years T 8 20 years (8 months) T 0 T 1 (20 months) T 70 T 71 T 72 P v of loan R (1+) (1 + ) & P v of payments (1 + ) B (1 + ) 71 (1 + ) 72.C F v of the payments (1 + ) + (1 + ) (1 + ) 72 SEE Q1.3 on p1.15 (Theory of nnutes) â.c â R3 016,6 1.2 Hre Purchase : The formula n ths case s slghtly dfferent - easy to see why! % 0,01 â 1 + 1,01 F v P v(1 + n) 8 % 3 016, (1 +.) â ,79 â. 0,79 â 0, â j 11,20% 2.1 The balance 75% of R R T 0 2 years T 2 (2 months) P v P v of payments -n 1-(1+) -2 1-B.C â j R1 383, 2.2 F v P v(1 + n) [1 + (0,13)(2)] R3 020 â Monthly payments 1. Loan : R ( P v!) P (1,02) - 3 P (1,02) - 6 P (1,02) - 10 P (1,02) - 20,7% 0,01725 â 1 + 1,01725 B R R1 17,50 MONEY LENDERS â P 1 + P 2 + P 3 + P â (1,02) ,25 â 3 933,25 % (1,02) R 988, F v P v(1 + n) [1 + (1)] â â 1,25 5% (m) eff 1+ (1 + 1,25) (2,25) â eff , % PYRMID SCHEMES eff (1 + 0,15) m (1,15) , â eff 1 32, % 2% 0,02 â 1 + 1,02 T 0 T 3 T 6 T The nomnal nterest rate s 15% PER WEEK! T