A zero$-$coupon bond is a bond that pay no interest payment. You buy the bond at a discount from the face value $($$$1000)$ and are paid the face amount when the bond matures.

A zero$-$coupon bond that will pay $$1,000$ in $10$ years is selling today for $$422\mathrm{.}41.$ What interest rate does the bond offer?

a$.$

$7\%$

b$.$

$8\%$

c$.$

$10\%$

d$.$

$9\%$