Suppose you manage a pension fund. Your projected pension liabilities in five years are $$14,693,000.$ You plan to invest $$10$ million today to meet this liability in five years, and you are trying to decide between buying bonds with five or six years to maturity. Both bonds have an $8\%$ annual coupon rate, $8\%$ yield to maturity, and you can buy enough of each bond such that the total par value is $$10,000,000.$

Calculate the duration of each bond.

For each bond, calculate the amount of money you will have after five years if interest remains $8\%($i$.$e$.,$ calculate the future value at time $5$; for the six year bond, you will have to estimate the selling price at time period $5).$ Does each bond provide sufficient cash to meet the liability?

For each bond, calculate the amount of money you will have after five years if interest rates immediately fall to $7\%$ after purchasing the bond. Do they provide sufficient cash to meet the pension liability?

For each bond, calculate how much money you will have after five years if interest rates rise to $9\%$ immediately after purchasing the bond. Do they provide sufficient cash to meet the pension liability?

If you are concerned about changes in interest rates, which bond would you choose? Briefly explain.