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:

Bond	Face Value ($)	Maturity (years)
A	1000	5
B	1000	10

Suppose the yield curve is flat at 5% for all maturities. Use annual compounding in this problem.

(a) What is the present value of the obligation to pay $1,000,000 in eight years?

(b) What are the prices and durations of bond A and B?

(c) How many of bonds A and B should you buy to fully immunise your obligation?

(d) If yields 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?

(e) 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.

(f) Will the bond portfolio still be a good immunizing portfolio for your obligation after 1 year? Assume the yield curve remains flat at 5%. Explain why.