Suppose the real risk$-$free rate is $3\mathrm{.}30\%$ and the future rate of inflation is expected to be constant at $2\mathrm{.}00\%.$ What rate of return would you expect on a $1-$year Treasury security, assuming the pure expectations theory is valid? Include cross$-$product terms, i$.$e$.,$ if averaging is required, use the geometric average. $($Round your final answer to $2$ decimal places.$)$

a$.5\mathrm{.}30\%$

b$.5\mathrm{.}37\%$

c$.3\mathrm{.}30\%$

d$.2\mathrm{.}07\%$

e$.3\mathrm{.}37\%$