The YTM on a bond is the interest rate you earn on your investment if interest rates don$$t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield $($HPY$).$

a$.$ Suppose that today you buy an annual coupon bond with a coupon rate of $8\mathrm{.}2$ percent for $$845.$ The bond has $10$ years to maturity and a par value of $$1,000.$ What rate of return do you expect to earn on your investment?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

b$-1.$ Two years from now, the YTM on your bond has declined by $1$ percent, and you decide to sell. What price will your bond sell for?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

b$-2.$ What is the HPY on your investment?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$