Please show all work and write down the equations you used!!!

Rosenworcel Corp. has a $$1,000$ par value bond with a $5\%$ coupon rate $($paid semiannually$)$ and a fifteen year maturity.

Let's assume that the market believes the Yield to Maturity on this bond should be $6\%.$

Assuming that the bond was just issued, calculate the current market price of the bond. $(1$ point$)$

a$.$ $$902\mathrm{.}00$

b$.$ $$1,238\mathrm{.}76$

c$.$ $$1,245\mathrm{.}27$

d$.$ $$1,392\mathrm{.}01$