Mr. Barnes wants to invest $100,000 for the next five years. He purchases an annuity from a

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Question:

Mr. Barnes wants to invest $100,000 for the next five years. He purchases an annuity from a financial institution. Currently the term structure is at 10% (continuously compounded).

(a) If the payments are made annually, what is the amount that the financial institution will agree to pay Mr. Barnes?

(b) Assume that there is a 5-year fixed coupon bond that pays coupons annually at a rate of 12% per annum. What is the price and duration of the bond?

(c) How much must the financial institution invest in the long-term bond in order to hedge the position? What should it do with the remainder of the money?