A $$6,000$ bond had a coupon rate of $5\mathrm{.}75\%$ with interest paid semi$-$annually. Peter purchased this bond when there were $7$ years left to maturity and when the market interest rate was $6\mathrm{.}00\%$ compounded semi$-$annually. She held the bond for $2$ years, then sold it when the market interest rate was $5\mathrm{.}50\%$ compounded semi$-$annually.

a$.$ Calculate the purchase price of the bond.

b$.$ Calculate the amount that Peter received when she sold the bond.