A $$6,500$ bond had a coupon rate of $4\mathrm{.}25\%$ with interest paid semi$-$annually. Anthony purchased this bond when there were $8$ years left to maturity and when the market interest rate was $4\mathrm{.}50\%$ compounded semi$-$annually. He held the bond for $4$ years, then sold it when the market interest rate was $4\mathrm{.}00\%$ compounded semi$-$annually.

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

$$6,391\mathrm{.}86$

Round to the nearest cent

b$.$ Calculate the amount that Anthony received when he sold the bond.

$$

Round to the nearest cent