A $$7,000$ bond had a coupon rate of $4\mathrm{.}75\%$ with interest paid semi$-$annually: Gabrielle purchased this bond when there were $7$ years left to maturity and when the market interest rate was $5\mathrm{.}00\%$ compounded semi$-$annually. She held the bond for $3$ years, then sold it when the market interest rate was $4\mathrm{.}50\%$ 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 Gabrielle's gain or loss on this investment?