An investor just purchased a semi$-$annual coupon bond with a coupon rate of $5\%$ and

$$1,000$ face value. The bond has a maturity is $20$ years, and its yield to maturity is $8\%.$

a$)$ Find the holding$-$period return for a one$-$year investment period if the bond is

selling at a yield of $6\%$ by the end of the year.

b$)$ If the investor sells the bond after one year, what taxes will he pay if the tax rate on

interest income is $30\%$ and the tax rate on capital gain income is $36\%?$

c$)$ What is the after$-$tax holding$-$period return on the bond?