Suppose now that you are a life insurance company projecting to pay benefits of $50 per year for the next 5 years to your policyholders, and then $110 per year for the next 5 years after that. The first $50 is to be delivered one year from now. You are operating in an economy where the term structure of interest rates is completely flat at 3%, so that all spot rates are 3%.

1. Calculate the present value of your benefit obligations.
2. Calculate the duration of your benefit obligations.
3. Given your calculation above, if you were choosing a single type of bond from 1-year, 2-year, 3-year, 4-year, 5-year, 6-year, 7-year, 8-year, 9-year, and 10-year zero coupon bonds, which would serve you best from the perspective of asset-liability matching? In other words, if interest rates were to change, which bonds price would move most closely with the present value of your obligations?
4. Imagine a 10 year bond paying annual coupons of $3 and a face value of $100. Using the duration-matching approach discussed in class, how many of these bonds (assume that you can purchase fractions of bonds) would you purchase to hedge your liabilities?
5. Calculate the percentage change in the value of your obligations if the interest rate were to drop from 3.0% to 2.9%.
6. Calculate the percentage change in the value of the bond in (4) if the interest rate were to drop from 3.0% to 2.9%.
7. Calculate the percentage change in the value of the bond identified in (3) if the interest rate were to drop from 3.0% to 2.9%.