An investor with a $5-$year investment horizon is considering purchasing a $15-$year $7\%$ coupon bond for $$913\mathrm{.}54.$ This means the YTM today is $8\%.$ The investor expects to be able to reinvest the coupon interest payments at an annual interest rate of $6\%($Please note that $6\%$ is a nominal rate, $3\%$ is the effective semi$-$annual interest rate that we should adopt$)$ and that at the end of the planned investment horizon, the then $10-$year bond will be selling to offer a YTM of $20\%.$

Please determine the projected bond price at the end of year $5.($The much higher YTM is usually due to the surge of credit risk$)$

Group of answer choices

$446\mathrm{.}62$

$652\mathrm{.}31$

$813\mathrm{.}07$

$1214\mathrm{.}30$