Amry and Karen have equal fund at the beginning. Using his fund, Amry purchases a 15-year annuity-due with annual payments of 3000 each. Karen puts her fund in an investment product earning effective rate of interest 7%. Three years later, she purchases a 12-year annuity immediate with annual payments of Z. The present values of both annuities are evaluated using an interest rate of 8%. (a) Calculate the present value of Karen's fund. (b) Evaluate the difference between Karen's and Amry's annual payment. [3 marks] [6 marks]