Assume all bonds have a face value of $100 and that all securities

are default-risk free. All cash flows occur at the end of the year to which they relate.

you observe the following: a 2-year coupon bond

paying 10% annual coupons with a market price of $97, and two annuities that

are trading at the same market price as each other. The first annuity matures in 3

years and pays annual cash flows of $20, while the second annuity pays annual

cash flows of $28 and matures in 2 years. Using this information:

i.

Complete the term structure of interest rates, i.e. determine the one- and

two-year discount factors, d1 and d2, respectively.

ii.

Determine the price of the annuities.