Question #$1$: Bonds $[20$ Points$]$

Use the following Scenario to answer Parts $($a$)-($c$)$

Suppose you're looking to purchase a $24$ year, $$1000$ face$-$value coupon bond that has a coupon rate of $3\mathrm{.}8\%.$ Assume that the current yield to maturity $($YTM$)$ is $4\mathrm{.}2\%$ 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 $4\mathrm{.}6\%.$ 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 yearfonsider 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? $[4$ Points$]$

Use the following Scenario to answer Part $($d$)$

$($d$)$ Assume that there is coupon bond that matures in $8$ years and pays $$1000$ at maturity. Suppose that the bond has a coupon rate of $5\mathrm{.}7\%$ and it makes an annual coupon payment. If the yield$-$to$-$maturity $($YTM$)$ is equal to $4\mathrm{.}5\%$ what is the current yield of the coupon bond? $[6$ Points$]$