GM Financing Inc. is planning to offer a $$1000$ par value $9-$year maturity bond with a coupon interest rate that changes every $3$ years. The coupon rate for the first three years is $10$ percent, $10\mathrm{.}75$ percent for the next $3$ years, and $11\mathrm{.}5$ percent for the final $3$ years. If you require an $11$ percent rate of return on a bond of this quality and maturity, what is the maximum price you would pay for the bond? $($Assume interest is paid annually at the end of each year.$)$

a$.$ $$875\mathrm{.}34$

b$.$ $$977\mathrm{.}63$

c$.$ $$621\mathrm{.}38$

d$.$ $$787\mathrm{.}49$