$($Related to Checkpoint $9\mathrm{.}4)($Bond valuation$)$ A bond that matures in $20$ years has a $$1,000$ par value. The annual coupon interest rate is $13$ percent and the market's required yield to maturity on a comparable$-$risk bond is $14$ percent. What would be the value of this bond if it paid interest annually? What would be the value of this bond if it paid interest semiannually?

a$.$ The value of this bond if it paid interest annually would be $$933\mathrm{.}7.($Round to the nearest cent.$)$

b$.$ The value of this bond if it paid interest semiannually would be $$939\mathrm{.}0.($Round to the nearest cent.$)$