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 $5\%.$

Please determine the projected bond price at the end of year $5.$

Hint: the implicit par value of this bond is $$1000.$ The implicit frequency of coupon payments is semi$-$annual.