DSC1630 ASSIGNMENT 1 SEMESTER | Questions And And Answers

DSC1630 ASSIGNMENT 1 SEMESTER 1 - 2020 | Questions And And AnswersDSC1630 ASSIGNMENT 1 SEMESTER 1 - 2020 DUE: 28 FEBRUARY 2020 2 Question 1 Precious borrows money from Steven at a simple discount rate of 9,75% per year. She must pay him R35 000 in 27 months’ time. The amount of money that she receives from Steven now is [1] R42 678,13. [2] R28 703,23. [3] R28 389,51. [4] R44 835,87. [5] R27 321,88. This is a simple discount calculation as the term discount rate is found in the question. The formula for simple discount is P = S(1 − dt). Given are the future value of the loan (S) which is R35 000, the time period which equals 27 months and the discount rate (d) of 9,75%. The time period that we use must always be in years. As the given time is in months we change it to a fraction of a year by dividing the months by the number of months in a year which is 12. Thus t = Now we need to determine the present value of the loan. Thus: P = S(1 − dt) = 35 000 (1 – 0.0975 × ) = R27 321.875…. 3 Question 2 On 29 March 2020, 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 2020 is [1] R3 643,09. [2] R3 649,06. [3] R3 637,88. [4] R3 640,24. [5] none of the above. 4 5 Question 3 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 [1] 10,50 years. [2] 3,25 years. [3] 7,19 years. [4] 4,65 years. [5] none of the above. 6 Question 4 The simple interest rate which is equal to a discount rate of 12% per year for a period of 18 months is [1] 14,63%. [2] 12,00%. [3] 0,12%. [4] 10,34%. [5] none of the above. 7 8 Question 5 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 [1] R18 080,24. [2] R14 117,08. [3] R18 865,83. [4] R18 988,31. [5] R15 690,19. 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 9 10 Question 6 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 [1] 17,68%. [2] 16,18%. [3] 17,18%. [4] 14,53%. [5] none of the above. 11 Question 7 Paul wants to buy a big screen TV. He has five interest rates to choose from if he borrows the money from the bank. The cheapest option for him is [1] 29% per year, compounded monthly. [2] 29,5% per year, compounded every two months. [3] 30% per year, compounded semi-annually. [4] 28,5% per year, compounded weekly. [5] 29% per year, compounded daily. The cheapest option will be the option with the smallest future value after one year. Choose any present value (P) let say R100, and time period (t), let us say one, and calculate the future value of each option. Remember the value m is the number of times the compounding is done in one year. 12 The cheapest option, or smallest as he borrows the money, for Paul is 30% per year, compounded semi-annually. 13 Question 8 The future value of a loan of R12 000 due in five years’ time, at a simple discount rate of 15% per annum is [1] R5 324,46. [2] R24 136,29. [3] R48 000,00. [4] R3 000,00. [5] none of the above. 14 Question 9 Fred won R165 000 and decided to deposit 65% of