DSC1630 Assignment 2 (DETAILED ANSWERS) Semester 2 2024 - DISTINCTION GUARANTEED

DSC1630 Assignment 2 (DETAILED ANSWERS) Semester 2 2024 - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED Answers, guidelines, workings and references .. Question 1 Complete Mark 1.00 out of 1.00 Question 2 Complete Mark 1.00 out of 1.00 QUIZ Mary invested R40 000 in order to have R56 000 available in 30 months’ time. The yearly rate, compounded semi-annually, is a. 7,21%. b. 8,00%. c. 13,92%. d. 14,41%. Bhongo received R32 412,87 after investing an amount of money in an account earning interest at a continuous compounding rate of 10,15%per year. The amount of money that he invested 57 weeks earlier, is approximately a. R29 000,00. b. R29 153,86. c. R32 768,16. d. R36 227,38. Question 3 Complete Mark 1.00 out of 1.00 Question 4 Complete Mark 1.00 out of 1.00 Question 5 Complete Mark 1.00 out of 1.00 To pay off a loan of R7 000 due now and a loan of R2 000 due in 14 months’ time, Mrs Skosana agrees to make three payments in two, fi ve andten months’ time respectively. The second payment is to be double the fi rst and the third payment is to be triple the fi rst. What is theapproximated size of the payment at month fi ve if interest is calculated at 16% per year, compounded monthly? a. R1 582,43 b. R3 000,00 c. R3 164,86 d. R4 500,00 Spiderman decides that he would like to buy his lovely wife, Spider woman, a new car when she turns 30 in six years’ time. He deposits R6 000 atthe beginning of each month into an account earning 8,94% interest per year, compounded monthly. The amount that Spider man (rounded tothe nearest rand) will have available six years from now is a. R333 412. b. R432 000. c. R568 948. d. R573 187. Thulani borrowed an amount of money from his father to open the Generous Grain Shop. The loan will be paid back by means of payments ofR25 000 each every second month for six years. An interest rate of 7,5% per year compounded every two months will be applicable. The presentvalue of the loan is a. R238 067,35. b. R400 738,72. c. R721 181,68. d. R900 000,00. Question 6 Complete Mark 1.00 out of 1.00 Question 7 Complete Mark 1.00 out of 1.00 Question 8 Complete Mark 1.00 out of 1.00 Quarterly deposits of R400 each are made into a bank account earning interest at 16% per year compounded quarterly. The approximate time(in number of quarters) that it will take for the account to accumulate to R40 000 is a. 41 quarters. b. 28 quarters. c. 2 quarters. d. 40 quarters. For four years Gundo paid R4 500 per month into a savings account earning 6,9% interest per year, compounded monthly. She then stopped hermonthly payments, but left the money in the account to earn more interest. It still earned 6,9% interest per year, but at that time thecompounding periods changed to quarterly. The balance in the account 10 years after she stopped her monthly payments, is a. R188 285,49. b. R216 000,00. c. R247 935,56. d. R491 413,14. An interest rate of 14,9% per year, compounded quarterly, is equivalent to a weekly compounded interest rate per year of a. 14,65%. b. 14,88%. c. 15,16%. d. 19,02%. Question 9 Complete Mark 1.00 out of 1.00 Question 10 Complete Mark 1.00 out of 1.00 Question 11 Complete Mark 1.00 out of 1.00 The accumulated sum of R12 000 invested at a continuous rate of 16,5% per annum for a period of fi ve years is a. R14 748,73. b. R23 217,51. c. R27 382,57. d. R36 049,99. On 5 April Lunga invested R75 000 in an account paying 8,37% interest per year, compounded monthly. Interest is credited on the 1st of everymonth. Lunga wants to open a second-hand cellphone shop in the new Talk-and- Listen complex. He will move into his new premises on 21November of the same year. If simple interest is used for odd period calculations and compound interest for the full term, then the amount of money that Lunga will haveavailable in the account on 21 November is a. R78 195,04. b. R78 955,68. c. R79 002,95. d. R79 020,96. On 5 April Lunga invested R75 000 in an account paying 8,37% interest per year, compounded monthly. Interest is credited on the 1st of everymonth. Lunga wants to open a second-hand cellphone shop in the new Talk-and-Listen complex. He will move into his new premises on 21November of the same year. If fractional compounding is used for the full term, then Lunga will receive on 21 November a. R78 439,73. b. R78 896,69. c. R79 020,29. d. R79 027,82. Question 12 Complete Mark 1.00 out of 1.00 Question 13 Complete Mark 1.00 out of 1.00 Question 14 Complete Mark 1.00 out of 1.00 Four years ago Karabo borrowed R120 000 from Ntsu at 12,65% per year, compounded quarterly, due two years from now. Six months ago, healso borrowed R65 000 from Ntsu at 15,2% per year compounded monthly due two years from now. The total amount that Karabo must pay Ntsu two years from now is a. R185 000,00. b. R285 408,03. c. R348 163,14. d. R385 752,04. Four years ago Karabo borrowed R120 000 from Ntsu at 12,65% per year, compounded quarterly, due twoyea rs from now. Six months ago, healso borrowed R65 000 from Ntsu at 15,2% per year compounded monthly due two years from now. After seeing what he owes Ntsu two years from now, Karabo decides to reschedule the debt. He will pay Ntsu R85 000 now and the rest fi veyears from now. Ntsu agrees on the condition that the new agreement will run from now, and will be subject to 13,7% interest per year,compounded half yearly. The amount that Karabo will pay Ntsu fi ve years from now is a. R164 878,56. b. R193 974,78. c. R354 164,34. d. R519 042,89. If R17 500 accumulates to R22 000 after 53 months, the continuous compounding interest rate is a. 5,18%. b. 5,19%. c. 5,32%. d. 5,82%. Question 15 Complete Mark 1.00 out of 1.00 A continuous compounding rate of 11,8% is equivalent to an effective rate of a. 11,15%. b. 11,80%. c. 12,52%. d. 43,06%.