DSC1630 Assignment 3 (QUALITY ANSWERS) Semester 1 2025

DSC1630 Assignment 3 (QUALITY ANSWERS) Semester 1 2025 DSC1630 Assignment 3 (QUALITY ANSWERS) Semester 1 2025.. Question 1Question 1 Not yet answered Marked out of 1.00 QUIZ Question 1 An interest rate of 17,5% per year, compounded quarterly, is equivalent to a continuous compounding rate of [1] 17,128%. [2] 17,185%. [3] 17,500%. [4] 17,888%. [5] 19,125%. Question 2 An amount borrowed at 29% interest per year, compounded continuously, has accumulated to R38 279,20 after four years. The initial amount borrowed was [1] R7 160,73. [2] R12 000,00. [3] R12 005,53. [4] R13 823,05. [5] R17 721,85. 20 2.2. COMPULSORY ASSIGNMENT 02 DSC1630/101 Question 3 The effective rate for a continuous compounding rate of 17,5% per year, is [1] 16,13%. [2] 17,50%. [3] 19,12%. [4] 19,13%. [5] 21,08%. Questions 4 and 5 relate to the following situation: An amount of R10 000 was invested in a special savings account on 15 May at an interest rate of 15% per annum, compounded quarterly for seven months. Interest is calculated on 1 January, 1 April, 1 July and 1 October of every year. Question 4 If simple interest is used for the odd periods and compound interest for the rest of the term, the amount of interest received after seven months is [1] R665,54. [2] R896,95. [3] R901,35. [4] R1 644,57. [5] none of the above. Question 5 If fractional compounding is used for the full term of seven months, the total amount of interest received is [1] R892,79. [2] R894,04. [3] R898,43. [4] R901,73. [5] none of the above. 21 DSC1630/101 CHAPTER 2. FIRST SEMESTER COMPULSORY ASSIGNMENTS Questions 6 and 7 relate to the following situation: Three years ago Jake borrowed R7 500 from Martha. The condition was that he would pay her back in seven years’ time at an interest rate of 11,21% per year, compounded semi-annually. Six months ago he also borrowed R25 000 from Martha at 9,45% per year, compounded monthly. Jake would like to pay off his debt four years from now. Question 6 The amount of money that Jake will have to pay Martha four years from now is [1] R36 607,98. [2] R45 181,81. [3] R48 032,20. [4] R54 278,92. [5] R55 336,49. Question 7 After seeing what he must pay Martha, Jake decides to reschedule his debt as two equal payments: one payment now and one three years from now. Martha agrees on condition that the new agreement, that will run from now, will be subjected to 10,67% interest, compounded quarterly. The amount that Jake will pay Martha three years from now is [1] R21 171,35. [2] R22 286,88. [3] R25 103,93. [4] R32 500,00. [5] none of the above. Question 8 If R35 000 accumulates to R48 320 at a continuous compounded rate of 8,6% per year, then the term under consideration is [1] 2,77 years. [2] 3,75 years. [3] 3,91 years. [4] 4,43 years. [5] 6,23 years. 22 Nicolet wants to buy a new state of the art computer for R35 000. She decides to save by depositing an amount of R500 once a month into an account earning 11,32% interest per year, compounded monthly. The approximate time it will take Nicolet to have R35 000 available is [1] 40 months. [2] 54 months. [3] 70 months. [4] 115 months. [5] none of the above. Question 10 If money is worth 12% per annum, compounded monthly, how long will it take the principal P to double? [1] 6,12 years [2] 7,27 years [3] 8,33 years [4] 69,66 years [5] None of the above Question 11 Paul decides to invest R140 000 into an account earning 13,5% interest per year, compounded quarterly. This new account allows him to withdraw an amount of money every quarter for 10 years after which time the account will be exhausted. The amount of money that Paul can withdraw every quarter is [1] R1 704,28. [2] R3 500,00. [3] R6 429,28. [4] R8 594,82. [5] none of the above. Question 12 If 15% per year, interest is compounded every two months, then the equivalent weekly compounded rate is [1] 14,464%. [2] 14,484%. [3] 14,816%. [4] 14,837%. [5] none of the above. 23 Question 13 Nkosi owes Peter R3 000 due 10 months from now, and R25 000 due 32 months from now. Nkosi asks Peter if he can discharge his obligations by two equal payments: one now and the other one 28 months from now. Peter agrees on condition that a 14,75% interest rate, compounded every two months, is applicable. The amount that Nkosi will pay Peter 28 months from now is approximately [1] R11 455. [2] R11 511. [3] R11 907. [4] R14 000. [5] R20 000. Question 14 The accumulated amount after eight years of monthly payments of R1 900 each into an account earning 9,7% interest per year, compounded monthly, is [1] R126 532,64. [2] R182 400,00. [3] R274 069,25. [4] R395 077,74. [5] none of the above. Question 15 A saving account pays interest at the rate of 5% per year, compounded semi-annually. The amount that should be deposited now so that R250 can be withdrawn at the end of every six months for the next 10 years is [1] R1 930,43. [2] R3 144,47. [3] R3 897,29. [4] R6 386,16. [5] none of the above. 24 Question 1 An amount of R600 is invested every month for eight years. The applicable interest rate is 14,65% per year, compounded quarterly. The accumulated amount of these monthly payments is approximately [1] R57 600. [2] R107 500. [3] R108 400. [4] R109 300. [5] R321 200. Question 2 At the beginning of each month an amount of X rand is deposited into a savings account earning k × 100% interest per year, compounded monthly. The future value of these savings after 24 deposits can be denoted by [1] S = Xs 24 k. [2] S = X(1 + k 12 )24. [3] S = (1 + k)Xs 24 k. [4] S = (1 + k 12 )Xs 24 k÷12. [5] none of the above. 25 Question 3 Bobby borrowed money that must be repaid in nine payments. The first four payments of R2 000 each are paid at the beginning of each year. Thereafter five payments of R5 000 each are paid at the end of each year. Note there is only one payment per year. If money is worth 6,85% per year, then the present value of these payments is [1] R22 588,92. [2] R23 054,54. [3] R27 381,02. [4] R27 845,64. [5] R33 000,00. Question 4 Amy is going to need R145 000 in three years’ time, to pay for a holiday overseas. She immediately starts to make monthly deposits into an account earning 11,05% interest per year, compounded monthly. Amy’s monthly deposit is [1] R3 384,18. [2] R3 415,34. [3] R4 027,78. [4] R4 707,20. [5] R4 750,55. Question 5 After an accident Charl was awarded an amount from the Accident Fund as compensation for his injuries. He chose to receive R18 900 per month indefinitely. If money is worth 9,95% per year, compounded monthly, then the amount awarded is approximately [1] R189 950. [2] R2 279 397. [3] R6 565 554. [4] R7 252 333. [5] none of the above. 26 2.3. COMPULSORY ASSIGNMENT 03 DSC1630/101 Questions 6 and 7 relate to the following situation: Solly will discharge a debt of R500 000 six years from now, using the sinking fund method. The debt’s interest is 15,6% per year, paid quarterly. The sinking fund earns interest at a rate of 8,4% per year, compounded monthly. Question 6 The monthly deposit into the sinking fund is [1] R4 236,10. [2] R5,364,60. [3] R10 736,10. [4] R12 958,53. [5] R16 235,96. Question 7 The total yearly cost to discharge the debt (to the nearest rand) is [1] R42 000. [2] R78 000. [3] R93 834. [4] R128 833. [5] R142 375. Question 8 Monthly deposits of R100 each are made into a bank account earning interest at an interest rate of 18% per annum, compounded monthly. The time (in months) that it will take the account to accumulate to R20 000 is given by [1] n = ln[200(0,015) + 1] ln(1 + 0,015) . [2] n = ln[200(1,015)] 0,015 . [3] n = ln[200(1,015) + 1] − ln(1,015). [4] n = ln[200(0,015) − 1] ln(1 + 1,015) . [5] none of the above. Questions 9, 10 and 11 relate to the following situation: The following is an extract from the amortisation schedule of a home loan: Month Outstanding Interest due Monthly Principal Outstanding principal at at month payment repaid principal at month beginning end month end 147 R8 155,83 A R2 080,54 R2 014,27 R6 141,56 148 R6 141,56 R49,90 R2 080,54 R2 030,64 B 149 B R33,40 R2 080,54 R2 047,14 R2 063,78 150 R2 063,78 R16,77 R2 080,54 R2 063,77 0 Question 9 The value of A is [1] R41,65. [2] R49,50. [3] R66,27. [4] R166,33. [5] R167,86. Question 10 The value of B is [1] R4 061,02. [2] R4 077,79. [3] R4 094,21. [4] R4 110,92. [5] R4 127,68. Question 11 If the interest rate has never changed, the original amount of the home loan (rounded to the nearest thousand rand) is [1] R21 000,00. [2] R180 000,00. [3] R310 000,00. [4] R312 000,00. [5] R606 000,00. 28 Questions 12 and 13 relate to the following situation: Jay intends to open a small material shop and borrows the money for it from his Uncle Jossop. Jay feels that he will only be able to start repaying his debt after three years. Jay will then pay Uncle Jossop R105 000 per year for five years. Money is worth 19,5% per year. Question 12 The present value of Jay’s debt at the time he will start paying Uncle Jossop back is [1] R222 924,04. [2] R317 500,78. [3] R408 978,93. [4] R436 649,07. [5] R525 000,00. Question 13 The amount of money that uncle Jossop originally lent Jay is [1] R98 346,23. [2] R130 288,26. [3] R130 633,09. [4] R184 589,43. [5] R186 054,89. Question 14 You are saving to pay for your children’s university costs in 20 years’ time. Your payment the first year is R3 600, after which your yearly payments increased by R360 each year. If the expected interest rate per year is 10%, the amount that you expect to receive to the nearest rand on the maturity date will be [1] R213 030. [2] R340 380. [3] R412 380. [4] R484 380. [5] none of the above. Question 15 Cindy bought a house and managed to secure a home loan for R790 000 with monthly payments of R9 680,70 at a fixed interest rate of 13,75% per year, compounded monthly, over a period of 20 years. If an average yearly inflation rate of 9,2% is expected, then the real cost of the loan (the difference between the total value of the loan and the actual principal borrowed) is [1] R87 126. [2] R201 642. [3] R270 749. [4] R588 358. [5] R1 060 749. 30 Question 1 The standard deviation for the number of houses sold is [1] 4,0. [2] 5,7. [3] 6,6. [4] 11,5. [5] none of the above. Question 2 The correlation coefficient of a linear regression between x and y is approximately [1] −0,16. [2] 0,16. [3] 4,00. [4] 5,72. [5] none of the above. 31 Questions 3 and 4 relate to the following situation: The following table represents the cash inflows of a boutique for nine years. Year Cash inflow (R) The applicable interest rate is 11,59% per year. The present value of the cash outflows is R95 000. Question 3 The future value of the cash inflows is approximately [1] R169 330. [2] R218 000. [3] R250 000. [4] R271 470. [5] R326 950. Question 4 The MIRR is [1] 14,72%. [2] 21,25%. [3] 31,90%. [4] 38,06%. [5] 41,91%. Question 5 Consider Bond F234 Coupon rate (half yearly) 10,5% per year Yield to maturity 7,955% per year Maturity date 8 October 2052 Settlement date 29 May 2018 The all-in-price is [1] R123,49852%. [2] R126,13814%. [3] R129,73733%. [4] R131,24248%. [5] R134,98733%. Question 6 The equation for the present value of Bond AAA on 17/06/2018 is given by 107,55174 = da n z + 1001 + 0,135 2 −29 . The yearly coupon rate is [1] 6,75%. [2] 7,35%. [3] 8,55%. [4] 14,70%. [5] none of the above. Questions 7 and 8 relate to the following situation: Consider Bond ABC Coupon rate: 9,75% per year Yield to maturity: 11,4% per year Maturity date: 15 April 2042 Settlement date: 29 November 2016 Question 7 The accrued interest is [1] R1,18207%. [2] R1,20205%. [3] R2,34537%. [4] R5,87781%. [5] none of the above. Question 8 The clean price is [1] R81,69720%. [2] R85,22964%. [3] R86,37296%. [4] R86,39294%. [5] R88,77706%. Question 9 If the NPV (Net Present Value) of a shop is R195 000 and the profitability index is 1,24375, the initial investment in the shop is [1] R86 908. [2] R156 784. [3] R195 000. [4] R800 000. [5] none of the above. Question 10 An estate agent suspects that there is a linear relationship between the number of houses sold and the monthly loan payments. She analyses the following data over the past six months. Number of houses Monthly loan sold payments (in R1 000’s) x y 160 3,7 250 5,6 800 7,5 450 11,3 120 18,9 50 28,4 The regression line equation is [1] y = −0,016x + 17,45. [2] y = 17,45x − 0,016. [3] y = −13,99x + 480,89. [4] y = 480,89x − 13,99. [5] none of the above. Question 11 The next coupon date that follows the settlement date of a bond is 28 October 2018. The half-yearly coupon rate is 7,375%. The accrued interest equals R5,49589%. If this is a cum interest case, the settlement date for this bond is [1] 14 June 2018. [2] 30 July 2018. [3] 29 August 2018. [4] 11 September 2018. [5] none of the above. Question 12 An investment with an initial outlay of R500 000 generates five successive annual cash inflows of R75 000, R190 000, R40 000, R150 000 and R180 000 respectively. The internal rate of return (IRR) is [1] 7,78%. [2] 9,48%. [3] 21,3%. [4] 27,0%. [5] none of the above. Question 13 The following figures show the profit of a greengrocer for the past five years: R360 000, R550 000, R200 000, R80 000 and R700 000. The arithmetic mean of the data is [1] R225 424. [2] R252 032. [3] R378 000. [4] R1 890 000. [5] none of the above. Question 14 You must choose between two investments, A and B. The profitability index (PI), net present value (NPV) and internal rate of return (IRR) of the two investments are as follows: Criteria Investment A Investment B NPV R44 000 −R22 000 PI 1,945 0,071 IRR 16,00% 8,04% Which investment(s) should you choose, taking all the above criteria into consideration, if the cost of capital is equal