1. 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]

2. Your daughter has just joined form three and is keen to join university immediately after completing high school to pursue her dream of studying interior design. As a forward looking parent you would like to invest part of your just received bonus payment as a lump sum in order to have university fees readily available when the time comes. You estimate that you will require KES 250,000 per year at the beginning of each university year (ignoring inflation) for the 5-year degree programme. (i.) How must should you invest as a lump sum now if you can earn a rate of interest 8% annually on investments? [4] (ii.) Suppose you opt to open a bank account that pays interest 5% per annum and deposit a level sum into it monthly for the next 7 years (2 years whilst she is still in high school and 5 years during her university education). How much would you need to deposit each month in order to have a nil balance in the account at the end of your daughters education? [You will also withdraw from this account annually to pay university fees.] [10]

3. An investor wishes to purchase a 10-year level annuity due that is payable half-yearly. The first payment will be made in 2 years. Calculate the amount of each payment if the purchase price is $10,000 and the effective interest rate is 8% pa.

4. Thanos, a powerful supervillain, believes that he will live forever and would like to purchase a perpetuity to provide him with a regular quarterly income as he causes chaos in the Marvel galaxy. Determine the amount of quarterly income he will receive if he pays a purchase price of $250Mn. Effective interest is 10% per annum. [3]

QUESTIONS 1 - 4