DSC1630 Assignment 2 (DETAILED ANSWERS Semester 1 2026 - DISTINCTION GUARANTEED

DSC1630 Assignment 2 (DETAILED ANSWERS Semester 1 2026 - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED Answers, guidelines, workings and references.. Questions 1 A loan will be paid back by means of payments of R250 each, every six month for ten years. An interest rate of 5% per year, compounded every six months, will be applicable. The present value of the loan is This problem has equal payments in equal time periods, plus the interest rate that is specified is compounded, See ordinary annuity hints. Questions 2 A nominal interest rate of 19,40% per year, compounded monthly, is equivalent to a continuous compounding rate of This is a conversion between two types of interest rates. Questions 3 An amount of money accumulates to R45 946 at a continuous compounding rate of 8% per year, after 57 months. The original amount is Questions 4 An interest rate of 14,90% per year, compounded every 3 months, is equivalent to a weekly compounded interest rate of Questions 5 Mohale deposits R1 500 at the end of every month into an account that earns 12,5% interest per year, compounded monthly. After two years, he stops making these monthly contributions because the interest rate changes to 15% per year, compounded every two months. If no withdrawals or deposits are made for the following four years, the balance in the account will be Questions 6 Mark want to buy a new gaming computer for R40 000. He decides to save by depositing an amount of R400 quarterly into an account earning 16% interest per year, compounded quarterly. The approximate number of quarters it will take Mark to have R40 000 available is Questions 7 Rendi decides that she would like to buy his daughter, Paige, a new car when she turns 30 in six years’ time. He deposits R6 000 each month into an account earning 8,94% interest per year, compounded monthly. The amount that Rendi (rounded to the nearest rand) will have available six years from now is Questions 9 If R35 000 accumulates to R48 320 at a continuous compounded rate of 8,6% per year, then the term under consideration is Questions 10 Mary needs R150 000 on 17 November 2026 to upgrade her deli. On 8 January 2026 she deposited an amount into an account earning 13,45% interest per year, compounded monthly, and being credited on the 1st of every month. If fractional compounding is used for the full term, then the amount that Mary deposited on 8 January 2026 was Questions 11 Six years ago Lusanda lent Siya R150 000 on condition that he would pay her back in nine years' time. The applicable interest rate is 15,5% per year, compounded monthly. Siya also owes Lusanda another amount of R250 000 that he has to pay back six years from now for a loan that earned interest at 16,4% per year, compounded semi-annually. Siya asks Lusanda if he can settle both his debts three years from now. The total amount that Siya will have to pay Lusanda three years from now is Questions 12 The continuous compounding rate is 13,974% per year. The equivalent nominal rate, compounded quarterly, is Questions 13 The Treasure Fund was created for Xiluva after she lost her leg in a battle with pirates. The fund has undertaken to pay her R1 200 000 now. Xiluva prefers to receive three payments: one three years from now; one twice the size of the first payment six years from now, and one four times the size of the first payment ten years from now. The amount of money to the nearest rand that Xiluva can expect to receive six years from now if the interest rate applicable is 8,6% per year, compounded quarterly, will be Questions 14 Three years ago Hulisani borrowed R10 000 from Simon on condition that she should pay him back two years from now. She also owes Simon R6 000 payable five years from now. The applicable interest rate for both transactions is 13,75% per year, compounded half yearly. After considering her payback schedule, Hulisani asks Simon if she can pay him R9 000 now and the rest in four years’ time. He agrees on condition that the new agreement will run from now and that an interest rate of 16,28% per year, compounded monthly, will be applicable from now. The amount that Hulisani will have to pay Simon four years from now is Questions 15 To pay off a loan of R7 000 due now and a loan of R2 000 due in 14 months’ time, Jabu agrees to make three payments in two, five and ten months’ time respectively. The second payment is to be double the first and the third payment is to be triple the first. What is the size of the payment at month five if interest is calculated at 16% per year, compounded monthly?