INSTRUCTION 191 151 2] ANSWER ALL QUESTIONS TOTAL MARKS: 40 Q.1. (A) 100 is deposited into an account at the beginning of every 4-year period for 40 years. The account credits interest at an annual effective rate of i. The accumulated value in the account at the end of 40 years is X, which is 5 times the accumulated value at the end of 20 years. Calculate X (B) i. The present value of a series of $5 at the end of every 5 years, forever, is equal to $20. Calculate the effective rate of interest, i. ii. What is the accumulated value of $9400 invested for 10 years after a 6% discount is paid at the beginning of the investment period? Q.2. (A) Madam Dora purchased a TV set for $550 and later decided to sell for $600. She sold it under the following hire purchase terms. An initial payment of 30% of the price and the balance paid in monthly equal installment at 10% simple interest per annum for 2 year. i. Calculate the amount paid every month ii. Calculate the amount the buyer paid for the TV set. iii. Calculate the percentage profit Madam Dora made on the cost price of the TV set. (B) An investment requires an initial payment of 10,000 cedis and annual payments of 1000 cedis at the end of each year of the years. Starting at the end of the cleventh year, the investment returns five equal annual payments of X. Determine the value of X to yield an annual effective rate interest over the 15-year period. (C) Let R denote a fixed regular payment made at the beginning of each year for n years. If R is invested at annual effective interest rate of i, i. Show that 5m 2/(1+i)" - 1] ii. Suppose that i = 10%, n=5 and R=$1000. Calculate 3301 [3] [3] [3] [7] d 121 INSTRUCTION 191 151 2] ANSWER ALL QUESTIONS TOTAL MARKS: 40 Q.1. (A) 100 is deposited into an account at the beginning of every 4-year period for 40 years. The account credits interest at an annual effective rate of i. The accumulated value in the account at the end of 40 years is X, which is 5 times the accumulated value at the end of 20 years. Calculate X (B) i. The present value of a series of $5 at the end of every 5 years, forever, is equal to $20. Calculate the effective rate of interest, i. ii. What is the accumulated value of $9400 invested for 10 years after a 6% discount is paid at the beginning of the investment period? Q.2. (A) Madam Dora purchased a TV set for $550 and later decided to sell for $600. She sold it under the following hire purchase terms. An initial payment of 30% of the price and the balance paid in monthly equal installment at 10% simple interest per annum for 2 year. i. Calculate the amount paid every month ii. Calculate the amount the buyer paid for the TV set. iii. Calculate the percentage profit Madam Dora made on the cost price of the TV set. (B) An investment requires an initial payment of 10,000 cedis and annual payments of 1000 cedis at the end of each year of the years. Starting at the end of the cleventh year, the investment returns five equal annual payments of X. Determine the value of X to yield an annual effective rate interest over the 15-year period. (C) Let R denote a fixed regular payment made at the beginning of each year for n years. If R is invested at annual effective interest rate of i, i. Show that 5m 2/(1+i)" - 1] ii. Suppose that i = 10%, n=5 and R=$1000. Calculate 3301 [3] [3] [3] [7] d 121