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 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.