(Actuarial Science)

8. Starting at age 50 a man deposits R800 p.a. quarterly in advance into a fund earning 7% p.a. compounded quarterly. The last deposit is made at age 54 years. On each of his 51st; 52nd; 53rd and 54th birthdays he withdraws R100 from this fund. At age 59, he purchases an annuity certain with the accumulated value of the fund. The annuity is payable quarterly in advance from age 60 to 70 inclusive. The annuity is calculated using an interest rate of 9% p.a. compounded monthly. Find: (a) The accumulated amount at age 59. (b) The quarterly payments made from age 60