Please answer and show steps thank you.

Problem 1 (10 points): A T-year par rate c(T) is the yield to maturity for a par bond (i.e., for a bond with the market price equal to its face value) that matures at time T. Use this definition and assume c(0.5)=5% and c(1)=6%

a) (3 points) Find a 1-year sport rate. Keep at least 6 decimal digits while doing calculations and reporting the answer.

b) (3 points) Find the price of a 1-year 7%-coupon bond. Round your answer to the nearest cent. Be very careful with your rounding - an error of $0.01 can lead to a significant penalty.

c) (2 points) Will the YTM on the bond in part (b) be higher or lower than 6%? Either compute this YTM (in which case you need to use a better than 1-cent precision for the bond price) or provide valid reasoning behind your answer.

d) (2 points) Assume that future interest rates are known today with 100% certainty (i.e., there is no volatility in future bond prices). Will the capital gain on the bond in part (b) over a 6-month holding period be positive or negative? Explain your reasoning without explicitly computing the future bond price (you may refer to other parameters such as coupon rate, par rates, YTM, etc).