A zero$-$coupon bond has a yield to maturity of $12\%$ and a par value of $$1,000.$ If the bond matures in $18$ years, the bond should sell for a price of today. $($Note: Assume annual compounding.$)$

Multiple Choice

$$130\mathrm{.}04$

$$501\mathrm{.}87$

$$422\mathrm{.}41$

$$513\mathrm{.}16$

None of the options are correct.