QUESTION 5 a) A man turns 30 today and wishes to deposit a lump sum, X, that will accumulate to provide his retirement fund of $40,000 paid to him at the beginning of each year starting on his 65th birthday. The fund will provide this payment until the last payment is made on his 75th birthday. The fund assumes annual interest rate of 8% Calculate X 18 mks b) Carl puts 10,000 into a bank account that pays an annual effective interest rate of 4% for ten years. If a withdrawal is made during the first five and, a penalty of 5% of the withdrawal amount is made. Carl withdrawals K at the end of year 4 and 5. The balance in the account at the end of year 10 is 10,000. Calculate K. 17 mks)