$.$ Bond Valuation. Consider a bond that matures in $3$ years. The face value

of this bond is $$1000.$ The bond pays semi$-$annual coupons at a rate of $8\%.$

$($a$)$ Calculate the price of this bond, assuming the yield to maturity is $8\mathrm{.}5\%$

$($b$)$ Suppose you hold this bond for two years and then sell it just after

receiving a coupon payment. At the time of the sale, the yield to maturity has

fallen to $7\mathrm{.}8\%.$ Calculate the price of the bond at the time of the sale.

$($c$)$ What is your total dollar value and percent return over the holding period?