It is estimated that inflation will average $5\mathrm{.}80\%$ per year for the next $4$ years, and average $4\mathrm{.}00\%$ each year thereafter. For a real risk$-$free rate of $2\mathrm{.}40\%,$ what is the default risk premium of a $12-$year corporate bond with a yield of $13\mathrm{.}80\%?$

Assume that the liquidity premium is $1\mathrm{.}40\%,$ but there is no maturity risk premium.

$5\mathrm{.}40\%$

$5\mathrm{.}56\%$

$5\mathrm{.}72\%$

$5\mathrm{.}02\%$

$4\mathrm{.}86\%$