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?

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