FINANCIAL MATHEMATICS 12 MARCH 2014

Transcription

1 FINNCIL MTHEMTICS 12 MRCH 2014 I ths lesso we: Lesso Descrpto Make use of logarthms to calculate the value of, the tme perod, the equato P1 or P1. Solve problems volvg preset value ad future value autes. Summary Smple Iterest The formula whch helps us to calculate the accumulated amout (future value) f a orgal amout s vested or loaed for years at a rate of r % smple terest s gve by: Compoud Iterest The formula whch helps us to calculate the accumulated amout (future value) f a orgal amout s vested or loaed for years at a rate of r % compoud terest s gve by: P( 1. ) P( 1 ) P = preset value of the vestmet or loa (orgal amout at the begg) = accumulated amout or future value of the vestmet or loa after perods r = 100 =tme perod s decmal form) for the smple terest rate r % ( FUTURE VLUE NNUITY P =preset value of the vestmet or loa (orgal amout at the begg) =accumulated amout or future value of the vestmet or loa after perods r = 100 =tme perod decmal form) for the smple terest rate r % ( s PRESENT VLUE NNUITIES x 1 F where : 1 x 1 1 P x paymet per perod x paymet per perod umber of paymets umber of paymets terest rate terest rate where :

2 Tmele Skg Fud T 0 T 1 T 2 T 3 T 4 T 5 The book value of a asset s ts value after deprecato has bee take to accout. The scrap value s the book value of a asset at the ed of ts useful lfe. The skg value s the fud set up to replace a asset at the ed of ts useful lfe. Compaes ofte purchase equpmet ad use t for a specfed tme perod. The old equpmet s the sold at scrap value ad ew, upgraded equpmet s bought. I order to face the purchasg of the ew equpmet, the compay wll have, well advace, set up a auty called a skg fud. skg fud s othg more tha a ormal savgs pla or future value auty. The proceeds from the skg fud ad the sale of the old equpmet are the used to purchase the ew equpmet. Skg Fud = Cost of ew mache Scrap value Cost of New Mache Scrap value Iflato P 1 Deprecato o reducg balace P 1 bass Balace of Loa Balace = Loa (Captal + terest accrued over years) repaymets for years (together wth terest) Balace P 1 Questo 1 1 x 1 Test Yourself vestmet of R9 000 ears 6% per aum compouded aually for a perod of 4 years. Thereafter, the terest rate chages to 7% per aum compouded aually for a further 2 years. Calculate the future value of the vestmet at the ed of the 6-year perod.. R13 518,69 B. R23 008,69 C. R13 008,69 D. R ,69 Questo 2 James vests R4 000 a bak accout payg 6% per aum compouded mothly. Calculate the value of hs vestmet 10 years tme.. R18 266,59 B. R8 166,59 C. R2 2666,50 D. R7 277,59

3 Questo 3 How much more moey would you have over a perod of 15 years o a savgs of R f the terest rate of 12% per aum was compouded mothly, as compared to a terest rate of 12% compouded aually?. R ,19 B. R ,95 C. R31 334,17 D. o dfferece. Questo 4 R5 000 s deposted to a savgs accout. The terest rate for the frst four years s 7% per aum compouded quarterly. Thereafter, the terest rate chages to 8% per aum compouded semaually. Calculate the value of the vestmet at the ed of the teth year.. R10 222,23 B. R23 645,23 C. R10 566,28 D. R11 456,11 Questo 5 Joseph deposts x to a savgs accout. Two years later, he deposts a further R2 to the accout. Three years after ths, he deposts 3x to the accout. The terest rate for the fve years s 18% per aum compouded mothly. He receves R at the ed of the fve year perod. Calculate the value of x.. R6 350,31 B. R4 452,32 C. R5 652,30 D. R6 230,51 Questo 6 vestmet of R9 000 ears 6% per aum compouded quarterly for a perod of 4 years. Thereafter, the terest rate chages to 7% per aum compouded sem-aually for a further 2 years. Calculate the future value of the vestmet at the ed of the 6-year perod.. R13 105,71 B. R12 235,62 C. R10 341,70 D. R18 900,50 Questo 7 a saves R6 000 a year ad deposts t at the ed of each year a savgs accout that pays her 7% p.a. compouded aually. Fd her accumulated savgs mmedately after the 12 th depost s made.. R ,71 B. R ,73 C. R ,72 D. R ,32

4 Questo 8 Fra buys a large house wth fve bedrooms. She plas to occupy oe room herself ad let the other rooms to teats. She expects the retal wll cover the loa repaymets o her house. She takes out a loa of R The terest o the loa s 8% compouded mothly. How much must she charge each teat f the loa s to be repad over 20 years?. R 1150,11 B. R 1261,12 C. R 1373,12 D. R 1000,17 Questo 9 Thado dreamt of becomg a mlloare. Whe she was 30 years old, she vested R wth a vestmet compay. If the terest rate was 8,5% p.a. compouded mothly, how old was she whe she acheved her dream? Gve your aswer correct to the earest year.. 50 years old B. 48 years old C. 49 years old D. 39 years old Questo 10 tax ower buys fve mbuses. Each bus costs hm R Determe the book value of the fleet of mbuses after four years f the deprecato s calculated at 20% p.a. o: a reducg balace.. R B. R C. R D. Noe of the above Questo 1 Improve your Sklls R3 000 s deposted to a savgs accout at a bak ad the terest pad s 15% p.a. compoud terest. fter how may years wll the vestmet be worth R5 250? Questo 2 Suppose R1 000 s deposted mmedately to a savgs accout ad cotues to make mothly paymets at the ed of each moth for a perod of 5 moths. Iterest s 18% p.a. compouded mothly. How much moey wll have accumulated at the ed of the 5 th moth? Questo 3 vestor aged 25 wshes to accumulate R by her 50 th brthday. She wll pay equal mothly paymets to a accout payg 15% per aum compouded mothly. Paymets start o her 25 th brthday ad ed o her 50 th brthday. Fd the mothly paymets. Questo 4 How much ca be borrowed ow f a perso agrees to repay a loa by meas of quarterly paymets of R7 000, startg three moths from ow? The paymets wll cotue for 3 years ad the terest rate s 16% per aum compouded quarterly. Questo 5 loa of R s to be repad by meas of mothly paymets of R5 000, startg oe moth after the gratg of the loa. Iterest s fxed at 18% per aum compouded mothly. How log wll t take to repay the loa?

5 Questo 6 school purchases a photocopyg mache for R The mache deprecates value at 22% p.a. o a reducg balace. The school wats to buy a ew mache 5 year s tme. ew mache wll cost much more the future ad ts cost wll escalate at 19% per aum effectve. The old mache wll be sold at scrap value after 5 years. skg fud s set up mmedately order to save up for the ew mache. The proceeds from the sale of the old mache wll be used together wth the skg fud ad the terest eared s 14,4% p.a. compouded mothly. The frst paymet wll be made mmedately ad the last paymet wll be made at the ed of the 5-year perod. a) Fd the scrap value of the old mache. b) Fd the cost of the ew mache 5 years from ow. c) Fd the amout requred the skg fud 5 years from ow. d) Fd the equal mothly paymets made to the skg fud. Questo 7 car s bought for R If 10% s pad cash ad the balace s pad usg a bak loa. The loa s repad over sx years. The terest rate s 10,5% p.a. compouded mothly. a) Determe the mothly repaymets. b) Determe the balace o the loa at the ed of two years mmedately after the 24 th paymet.