QUESTION 1: BASIC ANNUITIES AND APPLICATIONS [20 MARKS]

I.                   Find the present and future value of $1000 received every month end for 20 years if the interest rate is J12 = 12% p.a. (5 marks)

II.                 Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years. (5 marks).

III.               John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account? (10 Marks)