The following nominal default-free bonds are traded in a well functioning capital market today: (step by step work, no excel)

Bond Type face value coupon maturity price

A Zero Coupon Bond 100 ------ 1 year $95.00

B Coupon Bond 100 6% ------    2 years $97.92

C Coupon Bond 100 10% ------  3 years $104.44

1. Assuming that all the bonds make only annual payments, what discount factors (DF1, DF2, DF3) are embedded in these prices? Show all your calculations.(step by step work, no excel)

2.What is the effective annual interest rate that can be locked in today to borrow money in 1 year and repay it in 3 years? Assume this loan is default-free.

3.A bond is said to sell at par when its price is equal to its face value. Suppose that the U.S. government has decided to issue a 3-year coupon bond (with annual coupons) today. What should its coupon rate be for it to sell at par?

4.Suppose that you expect the rate of inflation to be 3% per year for each of the next three years. You are interested in a three-year “annuity” that would be “protected against inflation” in the sense that the payment received at the end of every year should give you the same purchasing power as $10,000 today.

(a) What nominal payments will this “annuity” make at the end of the first, second and third years?(step by step work, no excel)

(b) Using the default-free term structure and the rate of inflation, what is the price today of this “annuity”?