a) Betty received $ 500,000 from a life insurance policy to be distributed to her as an annuity certain in 10 equal annual installments with the first payment made immediately. On the day she receives her third payment, she is offered a monthly perpetuity of X in lieu of the future annual payments. The first payment will be made in exactly one month. The effective annual rate of interest is 8 %. Determine the value of X.

b) Two perpetuities have the same annual effective interest rate. Perpetuity A pays $ 12 at the end of each year for the first 20 years and then $ 6 at the end of each year thereafter. Perpetuity B is a perpetuity due which has a level annual payment of $ 9. At time t=0t=0, the present value of Perpetuity A is equal to that of Perpetuity B. What is the effective annual interest rate, ii?