You have a liability for paying college fees for your children of $20,000 at the end of each of the next 2 years (2024-2025). You can invest your money now (January 1 2024) in 2 different types of investments: 1-year zero-coupon bonds, and 4-year zero-coupon bonds. Both have a yield to maturity of 8%, compounded semi-annually.

a. How much do you have to put aside today, assuming that interest rates stay unchanged?

b. Suppose you invest all the money you need to put aside (the amount just computed) in the 4-year bonds today, and then sell the appropriate amount for the fee payments. Show that if interest rates remain unchanged, you will meet your obligations exactly. Now consider the case where interest rates change only once, immediately after you made your investment. They can either rise to 9% or drop to 7%. If you continue to meet your payments, then how much are you short (or how much have you left over) immediately after you made the second payment?

c. Suppose now you invest all the money you decided to put aside into the 1-year zero coupon bonds, then make your fee payment and reinvest the remainder. Show that if interest rates remain unchanged, you will meet your obligations exactly. Now consider the case where interest rates change only once, immediately after you made your investment. They can either rise to 9% or drop to 7%. What is the result now? Compare your results with those under b) and comment.