Suppose the real risk$-$free rate of interest is $2\%.$ Inflation is expected to be $2\%$ for $2$ years and then $3\%$ thereafter. The maturity risk premium is $0\mathrm{.}2\%(t).$ where $t$ is the number of years until maturity. The default risk premium is $2\%.$ The liquidity premium is $1\%.$ What is the nominal interest rate on a $4$ year bond?

$9\mathrm{.}1\%$

$7\mathrm{.}8\%$

$71\%$

$8\mathrm{.}3\%$