QUESTION FOUR. A. On the basis of the following force of interest

2

0.05 0.025 0 4 0.015 0.04 4 t for t

t

t t

(i.) Calculate the amount to which 1,000 will have accumulated at t = 7 if it is invested at t = 3 [4] (ii.) Calculate the constant force of interest per annum that would give rise to the same accumulation from time t = 0 to time t = 7. [5] C. Mrs Okoth invests a sum of money for her retirement which is expected to be in 20 years time. The money is invested in a zero coupon bond which provides a return of 8% per annum effective. At retirement, she requires sufficient money to purchase an annuity certain of KES 1,200,000 per annum for 25 years. The annuity will be paid monthly in arrear and the purchase price will be calculated at a rate of interest of 6% per annum convertible half-yearly. (i.) Calculate the sum of money she needs to invest at the beginning of the 20-year period. [7] Over the 20-year period the Consumer Price Index has changed in value from 103 at the beginning of the 20-year period to 353 at the end of the 20-year period (ii.) Calculate the annual effective real return Mrs Okoth would obtain from the zero coupon bond. [4] [20 Marks]