$($Cost of debt$)$ Sincere Stationery Corporation needs to raise $$467,000$ to improve its manufacturing plant. It has decided to issue a $$1,000$ par value bond with an annual coupon rate of $10\mathrm{.}4$ percent with interest paid semiannually and a $15-$year maturity. Investors require a rate of return of $7\mathrm{.}8$ percent.

a$.$ Compute the market value of the bonds.

b$.$ How many bonds will the firm have to issue to receive the needed funds?

c$.$ What is the firm's after$-$tax cost of debt if the firm's tax rate is $34$ percent?

a$.$ The market value of the bonds is $ $($Round to the nearest cent.$)$