1. (a)

Karan has 20,000 and intends to purchase an annuity. The following two annuities are available:

- X paid annually in arrear for 15 years; or

- Y paid annually in advance for 15 years.

Calculate X and Y assuming an effective interest rate of 5.25% per annum.

(b) Droddy is a university student. He has won a three-year scholarship to pay his tuition fees. The payments under the scholarship are as follows:

- Year 1: 9,000 per annum paid continuously - Year 2: 9,000 per annum paid monthly in advance. - Year 3: 9,000 per annum paid half-yearly in arrears

Calculate the total present value of these payments at the beginning of the first year, using a nominal rate of interest of 6% per annum convertible quarterly.