A $2-$year Treasury bond has a $4\mathrm{.}00\%$ yield. A $5-$year Treasury bond yields $6\mathrm{.}00\%,$ and a $5-$year corporate bond yields $37\mathrm{.}40\%.$ The market expects that inflation will average $3\mathrm{.}0\%$ over the next $5$ years. Assume that MRP $=[0\mathrm{.}10$ x $($t$-1)]\%,$ where t is the number of years to maturity. Also assume that the annual real risk$-$free rate will remain constant over the next $5$ years.

A $2-$year corporate bond has the same default risk premium and liquidity premium as the $5-$year corporate bond described. What is the yield on this $2-$year corporate bond?