Bond X$,$ Bond Y$,$ and Bond Z are each n$-$year bonds with face amount $1,000.$ All three bonds are priced to yield a nominal annual interest rate of $6\mathrm{.}5\%$ convertible semiannually.

Bond X provides annual coupons of R$,$ Bond Y provides quarterly coupons of $20\mathrm{.}00,$ and Bond Z provides semiannual coupons of $32\mathrm{.}50.$

The price of Bond Y exceeds the price of Bond X by $401\mathrm{.}50$ and the price of Bond Y exceeds the price of Bond Z by $169\mathrm{.}30.$

Calculate R$.$

A

$41\mathrm{.}76$

B

$42\mathrm{.}03$

C

$43\mathrm{.}78$

D

$44\mathrm{.}25$

E

$45\mathrm{.}52$