The real risk$-$free rate is $2\%.$ Inflation is expected to be $4\%$ this year, $3\%$ next year, and $2\mathrm{.}4\%$ per year thereafter. The maturity risk premium is estimated to be $0\mathrm{.}05(t-1)\%,$ where $t=$ number of years to maturity. The default risk premium and liquidity premium on a AAA bond are $0\mathrm{.}4\%$ and $0\mathrm{.}2\%,$ respectively. What is the yield on a $5-$year Treasury security?

a$.5\mathrm{.}44$

b$.5\mathrm{.}64$

$K=K**+IP+MRP$

c$.5\mathrm{.}84$

d$.5\mathrm{.}04$

$1yr=2+4$

e$.3\mathrm{.}20$