You have an obligation to pay $1,000,000 in eight years from now, and you would like to make an investment now that will enable you to meet this obligation. This investment will be a portfolio containing two of the following zero-coupon bonds: Zero coupon Bonds Available to Purchase Bond Face Value Yield to maturity Maturity Price A $100 6% 5 years $74.73 10 years $55.84 B $100 6% a) What is the present value of the obligation to pay $1,000,000 in eight years? b) How many of bonds A and B should you buy to fully immunise your obligation? c) If the yields suddenly rise by 1% for all maturities, by what percentage (approximately) will the value of your hedging portfolio (the bonds only, not the $1,000,000 obligation) change? d) Will your estimate in the previous question tend to over-state, under-state or perfectly estimate the percentage change in the bond prices? Explain why.