Suppose you have bought an annuity that will guarantee to pay you $100,000/year for 10 years. The first payment will be five years from today. The bank that sells me this annuity is worried about interest rate risk and want to immunize its position (obligations). Show calculations (not excel)

a. Assuming the current interest rate is 8%, what is the duration of this annuity (the banks obligation)?

b. The manager is planning to use a 5-year and a 15-year zero coupon bond to immunize banks position. Assuming an 8% yield, how much money should be invested in each bond? What would be the face value (par value) of each bond?