DSC1630 - Introductory Financial Mathematics_ASSIGNMENT_2_SEMESTER_1.

DSC1630 - Introductory Financial Mathematics_ASSIGNMENT_2_SEMESTER_1. Question 1 Shona decides that he would like to buy his lovely wife, Connie, 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 Shona (rounded to the nearest rand) will have available six years from now is [1] R568 948. [2] R573 187. [3] R333 412. [4] R335 896. [5] R432 000. In this problem we have equal payments in equal time periods (monthly), plus the interest rate is specified as compounded, thus we are working with annuities. We need to determine the future value of an ordinary annuity. Shona will have R568 948 available 3 Question 2 An amount of money accumulates to R45 946 at a continuous compounding rate of 8% per year, after 57 months. The original amount is [1] R31 460,34. [2] R33 294,20. [3] R36 756,80. [4] R31 420,70. [5] R28 486,52. 4 Question 3 Allan 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 Allan to have R40 000 available is [1] 2 quarters. [2] 12 quarters. [3] 40 quarters. [4] 41 quarters. [5] 28 quarters. 5 Question 4 An interest rate of 14,90% per year, compounded every 3 months, is equivalent to a weekly compounded interest rate of [1] 15,16%. [2] 14,65%. [3] 19,02%. [4] 14,88%. [5] none of the above. 6 7 Question 5 Martha needs R150 000 on 17 November 2020 to upgrade her deli. On 8 January 2020 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 Martha deposited on 8 January 2020 was [1] R168 276,24. [2] R168 230,00. [3] R133 745,47. [4] R133 708,72. [5] R133 663,53. 8 Martha deposited R133 708,72 on 8 January 2020. Question 6 Luke deposits R1 500 at the end of every month into an account that earns 12,5% interest per year, com- pounded 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 four years the balance in the account will be [1] R72 517,49. [2] R40 660,72. [3] R65 114,13. [4] R62 224,96. [5] R73 544,10. 9 10 Question 7 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. 11 The term under consideration is approximately 3,75 years Question 8 Six years ago Martha lent Jake 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. Jake also owes Martha 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. Jake asks Martha if he can settle both his debts three years from now. The total amount that Jake will have to pay Martha three years from now is [1] R400 000,00. [2] R475 017,72. [3] R488 092,15. [4] R755 667,10. [5] R777 202,69.