You are considering a $13-$year, $$1,000$ par value bond. Its coupon rate is $10\mathrm{.}50\%,$ and interest is paid semiannually. If you require an "effective" annual interest rate of $10\mathrm{.}90\%,$ how much should you be willing to pay for the bond?

$$972\mathrm{.}54$

$$972\mathrm{.}86$

$$1,000\mathrm{.}00$

$$991\mathrm{.}87$

$$991\mathrm{.}77$