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

DSC1630 Assignment 1 (DETAILED ANSWERS Semester 1 2026 - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED Answers, guidelines, workings and references.. Question 1 Hassim deposits R900 into a savings account paying 6,5% interest per year, compounded quarterly. After three and a half years he withdraws R1 000 from the account and deposits it into a second account paying 11% simple interest per year. How much is the total amount accrued in the first account two years after withdrawing the R1 000? The correct answer, rounded to the nearest rand, is Refer to Paragraph 2.2 on timelines in the study material. Question 2 Hassim deposits R900 into a savings account paying 6,5% interest per year, compounded quarterly. After three and a half years he withdraws R1 000 from the account and deposits it into a second account paying 11% simple interest per year. A number of years after Kariem deposited the R1 000 into the second account, the accrued amount in the second account is R1 605. The time (correct to two decimal places) the money was invested for is Downloaded by Polar magnats () lOMoARcPSD| DSC Sem1 HAS1 page 4 Refer to Paragraph 2.2 on timelines in the study material. Question 3 An effective rate of 29,61% corresponds to a nominal rate, compounded weekly, of This is a conversion between two types of interest rates since one is asked to express the nominal interest rate in terms of the effective interest rate. See hints numbers 3.1 and 3.2 above. Question 4 An investment of R20 000 accumulated to R45 200. If the applicable simple interest rate is 12% per year, then the time under consideration is See hints 3.1 above. Question 5 Anna won R165 000 and decided to deposit 65% of this amount in an account earning 8,25% interest per year, compounded every four months. The accumulated amount after five years is Refer to Paragraph 2.2 on timelines in the study material, also refer to hint 2 above. Question 6 Calculate the present value of a loan of R12 000 due in five years’ time, at a simple discount rate of 15% per annum is See hint number 2 above. Question 7 Mondlana borrowed R500 from Grace four months ago and R700 nine months ago. He wants to liquidate these obligations with a single payment in 12 months’ from now. If a simple interest rate of 11% per year, is charged on all the amounts, the amount he will pay Grace in 12 months’ from now is This is a simple interest calculation as the words simple interest rate are found in the question. As there are quite a few things that are taking place it is very important to draw a timeline of the problem to help you understand the problem better. Refer to Paragraph 2.2 on timelines in the study material. Downloaded by Polar magnats () lOMoARcPSD| DSC Sem1 HAS1 page 5 Question 8 Phuti receives R1 500,00 from the bank now that charge 10,5% simple discount per annum. She has to pay back the bank an amount of R1 893,75 in a few months’ time. The number of months after which Emily pays back the loan, rounded to one decimal place, is See hints numbers 2. Question 9 Having received a large inheritance, Joseph’s parents wish to establish a trust for his university education. They need an estimated R70 000, 15 years from now. The amount they should set aside in the trust now, if they invest the money at 18,5% per year compounded quarterly, is See hints numbers 2 and 3 above. Question 10 Michael wants to buy a double door refrigerator. He has five interest rates to choose from if he borrows the money from the bank. The cheapest option for him is See ID words above and hint 3.1. Question 11 On 29 March 2026, Frieda deposited R3 500 into a savings account. The simple interest rate agreed upon was 7,5% per year. The accumulated amount in the savings account on 10 October 2026 is Note: Ignore the leap year unless it is specified that it is a leap year. See hint number 2 above. Question 12 The accumulated amount that you will receive after 38 months if you deposit R13 300 into an account where money is worth 11,35% per year, compounded every two months is See hint number 2 above. Downloaded by Polar magnats () lOMoARcPSD| DSC Sem1 HAS1 page 6 Question 13 The bank charges a nominal interest rate is 16,5% per annum, compounded at the end of every second month. The equivalent effective interest rate is This is a conversion between two types of interest rates since it is asked to write the effective rate in terms of the nominal rate. See ID words above. Question 14 The simple interest rate which is equal to a discount rate of 12% per year for a period of 18 months is The terms simple interest and simple discount are found in the wording of the problem. Thus if it was just a simple interest rate calculation the formula used would have been S = P(1 + rt). If it was only a simple discount calculation the formula used would have been P = S(1 − dt). Now as both simple interest and simple discount are mentioned, we need a formula that expresses the relationship between the two. In the solution of Exercise 2.3.2 in the guide, we derived a formula for the relationship between the simple interest rate and the simple discount rate as being,