The real risk$-$free rate, $r^{**},$ equals $2\%.$ Inflation is expected to be $2\%$ per year over the next five years and then $3\%$ per year thereafter. The maturity risk premium $($MRP$)$ equals $0\mathrm{.}05\%(t-1),$ where $t=$ the maturity of the bond. A $10-$year corporate bond has a yield of $7\mathrm{.}8\%.$ A $12-$year corporate bond has the same default risk and liquidity premiums as the $10-$year corporate bond. What is the yield on the $12-$year bond? Disregard cross$-$product terms, i$.$e$.,$ if averaging is required, use the arithmetic average.

$7\mathrm{.}48\%$

$7\mathrm{.}90\%$

$8\mathrm{.}50\%$

$7\mathrm{.}98\%$

$8\mathrm{.}30\%$