You consider issuing a 4-year bond which, unlike normal bonds, does not pay any face value at maturity. The bond only pays coupons that grow at a rate of 5% each year. For instance, the first coupon, paid at the end of year one, is $1,000(1 + 0.05), the second is $1,000(1 + 0.05)^2 , and so on. The current interest rate is 5%, and the yield curve is flat.

1. What is the present value of the bond?

2. What is the duration of the bond?

3. You sold $5 mil. worth of bonds. You now want to invest the proceeds you raise in two assets: a 12-month Treasury Bill (A1) and a 4-year zero-coupon bond (A2). How much should you invest in each asset to avoid any duration mismatch?