Suppose you$$re looking to purchase a $15$ year, $$1000$ face$-$value coupon bond that has a coupon rate of

$6\mathrm{.}5\%.$ Assume that the current yield to maturity $($YTM$)$ is $5\mathrm{.}8\%$ and that the coupon payments are paid

semi$-$annually.

$($a$)$ What is the price you would pay for this bond today? Round your answer to two decimal places.

$[5$ Points$]$

$($b$)$ Suppose next year the YTM increases to $6\mathrm{.}8\%.$ What would be the price of the bond that you purchased

in Part $($a$)$ next year? $[$Hint: When calculating the price of the bond next year consider how many periods

are left until the bond matures.$]$ Round your answer to two decimal places. $[5$ Points$]$

$($c$)$ Suppose you decide to sell the bond next year at the price you found in Part $($b$).$ What would be your

$1$ year holding period return on the bond?