Mr Brown Wants to Invest $100,000 for the Next ?Ve

Essay

Mr. Brown wants to invest $100,000 for the next ?ve years. He purchases an annuity from a ?nancial institution. Currently the term structure is ?at at 10% (yearly compounded).
i. If the payments are made yearly, what is the amount that the ?nan- cial institution will agree to pay Mr. Brown?
ii. Assume that there is a 5-year ?xed coupon bond that pays 12% coupon every year. What is the price and duration of the bond?
iii. How much must the ?nancial institution invest in the long-term bond in order to hedge the position? What should it do with the remainder of the money?