actuarial science

At time 0, the term structure of effective annual yield rates for zero coupon bonds is given as follows:

1- and 2-year maturity: 10%

3- and 4-year maturity: 12%

(a) Determine the price of a 4-year annual coupon bond with face amount 100 and coupon rate 5%.

(b) You are given that the price of a 5-year annual coupon bond with face amount 100 and coupon rate 5% is 75. Determine the forward effective annual interest rate for the period from time 4 to time 5, i.e., f[4,5].

(c) A lender offers to lend you 1000 for one year at rate 10% starting two year from now. Construct transactions that provide an arbitrage gain and give the amount of the gain.