A $$6,000$ bond had a coupon rate of $5\mathrm{.}75\%$ with interest paid semi$-$annually. Samantha

purchased this bond when there were $8$ years left to maturity and when the market

interest rate was $6\mathrm{.}00\%$ compounded semi$-$annually. She held the bond for $3$ years,

then sold it when the market interest rate was $5\mathrm{.}50\%$ compounded semi$-$annually.

a$.$ What was the purchase price of the bond? b$.$whata was the selling price of the bond? c$.$ what was samanthas gain or loss on this investment?