You have been asked to value a $40-$year bond, issued by StayCool Corporation, with the following features. The coupon rate for the first $20$ years will be $6\%$ of the face value of $$1,000.$ After $20$ years, the coupon rate will increase to $7\%$ for the remaining $20$ years. Estimate the value of this bond, if StayCool is rated AA$.($AA$-$rated bonds are trading at a default spread of $0\mathrm{.}50\%$ over the Treasury bond rate of $6\mathrm{.}50\%.)$

a$.$ $$1,098$

b$.$ $$1,054$

c$.$ $$976$

d$.$ $$894$

e$.$ None of the above, the answer is $ $\_\_\_\_\_\_\_\_\_.$