MATHEMATICS GRADE SESSION 3 (LEARNER NOTES) TOPIC 1: FINANCIAL MATHEMATICS (A) Learer Note: Ths sesso o Facal Mathematcs wll deal wth future ad preset value autes. A future value auty s a savgs pla for the future, whereas a preset value auty s a loa. There are two types of loas dealt wth ths sesso. The frst loa s oe whch you borrow moey from a bak ad have to pay a certa umber of equal repaymets wth terest. The secod type of loa s oe whch you depost a large sum of moey to the bak ad the bak pays you equal amouts wth terest over a gve tme perod. SECTION A: TYPICAL EXAM QUESTIONS (10 mutes) (b) Suppose that at the begg of the moth, R1000 s deposted to a bak. At the ed of that moth, a further R1000 s deposted ad a further R1000 at the ed of the ext moth. Ths cotues for eght years. If the terest rate s 6% per aum compouded mothly, how much wll have bee saved after the eght year perod? Patrck decded to start savg moey for a perod of eght years startg o 31 December 009. At the ed of Jauary 010 ( oe moth s tme), he deposted R300 to the savgs pla. Thereafter, he cotued makg deposts of R300 at the ed of each moth for the plaed eght year perod. The terest rate remaed fxed at 10% per aum compouded mothly. (1) How much wll he have saved at the ed of hs eght year pla whch started o the 31 December 009? () If Patrck leaves the accumulated amout the bak for a further three moths, what wll the vestmet the be worth? [16] QUESTION 10 mutes Davd takes out a bak loa to pay for hs ew car. He repays the loa by meas of mothly paymets of R4000 for a perod of fve years startg oe moth after the gratg of the loa. The terest rate s 4% per aum compouded mothly. Calculate the purchase prce of hs ew car. (b) Peter herts R400 000 from hs father. He vests the moey at a terest rate of % per aum compouded mothly. He wshes to ear a mothly salary from the vestmet for a perod of twety years startg oe moth s tme. How much wll he receve each moth? [8] Page 1 of 5
MATHEMATICS GRADE SESSION 3 (LEARNER NOTES) SECTION B: ADDITIONAL CONTENT NOTES Future value auty formula: x(1 ) 1 F where: x equal ad regular paymet per perod umber of paymets r terest rate as a decmal 100 Learer Note: Ths formula deals wth savg moey for the future. Remember that the value of represets the umber of paymets ad ot ecessarly the durato of the vestmet. Preset value auty formula: x1 (1 ) P where: x equal ad regular paymet per perod umber of paymets r terest rate as a decmal 100 Learer Note: Ths formula deals wth loas. There must always be a gap betwee the loa ad the frst paymet for the formula to work. SECTION C: HOMEWORK Mpho takes out a retremet auty that wll supplemet hs peso whe he retres thrty years tme. He estmates that he wll eed R 500 000 ths retremet fud at that stage. The terest rate he ears s 9% per aum compouded mothly. Calculate hs mothly paymet to ths fud f he starts payg mmedately ad makes hs fal paymet 30 years tme. (5) Page of 5
MATHEMATICS GRADE SESSION 3 (LEARNER NOTES) (b) The retremet fud does ot pay out the R 500 000 mllo whe Mpho retres. Istead he wll be pad mothly amouts, for a perod of twety years, startg oe moth after hs retremet. If the terest that he ears over ths perod s calculated at 7% per aum compouded mothly, determe the mothly paymets he wll receve. (5) [10 QUESTION Smphwe takes out a twety year loa of R100 000. She repays the loa by meas of equal mothly paymets startg three moths after the gratg of the loa. The terest rate s 18% per aum compouded mothly. Calculate the mothly paymets. [5] SECTION D: SOLUTIONS AND HINTS TO SECTION A Draw a tmele x(1 ) 1 F 97 0,06 1000 1 1 F 0,06 F R4 44,68 I ths example, the durato of the loa s 8 years ( moths). However, the umber of paymets made s 97 because of the frst paymet beg made mmedately. Ths meas that the frst moth, two paymets of R1000 were made. correct formula 97 0,06 aswer Page 3 of 5
MATHEMATICS GRADE SESSION 3 (LEARNER NOTES) (b)(1) Draw a tmele (b)(1) x(1 ) 1 F 0,10 300 1 1 F 0,10 F R336 16,47 I ths example, the durato of the loa s 8 years ( moths). However, the umber of paymets made s because of the frst paymet beg made oe moth after the start of the savgs pla. correct formula 0,10 aswer (b)() Draw a tmele 336 16,47 1 T T97 T98 T99 (b)() A P(1 ) 0,10 A 336 16,471 A R344 69, 3 Sce there wll o loger be ay further paymets of R300 to the auty, all we ow eed to do s grow the R336 16,47 for three moths usg the formula A P(1 ) to calculate the future value of the vestmet after the further three moths. correct formula 3 P 336 16,47 aswer Page 4 of 5
MATHEMATICS GRADE SESSION 3 (LEARNER NOTES) QUESTION Draw a tmele 60 x 1 (1 ) P 0,4 4000 1 1 P 0,4 P R139043,55 60 There must always be a gap betwee the loa (P) ad the frst paymet order for the preset value formula to work. correct formula 60 0,4 0,0 aswer (b) Draw a tmele 3 40 T (b) 40 0, x 11 400000 0, 4000000, 01 x 40 1 (1, 01) x R4404,34 Ths s a example of a loa where you pay moey to a bak ad the bak pays you mothly amouts wth terest. correct formula 40 0, 0,01 aswer The SSIP s supported by Page 5 of 5