A $$8,500$ bond had a coupon rate of $5\mathrm{.}50\%$ with interest paid semi$-$annually. Sarah purchased this bond when there were $7$ years left to maturity and when the market interest rate was $5\mathrm{.}75\%$ compounded semi$-$annually. He held the bond for $3$ years, then sold it when the market interest rate was $5\mathrm{.}25\%$ compounded semi$-$annually.

a$.$ What was the purchase price of the bond?

Round to the nearest cent.

b$.$ What was the selling price of the bond?

Round to the nearest cent.

c$.$ What was Sarah's gain or loss on this investment?