Suppose the real risk$-$free rate is $4\mathrm{.}10\%$ and the future rate of inflation is expected to be constant at $2\mathrm{.}10\%.$ 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$.2\mathrm{.}19\%$

b$.6\mathrm{.}29\%$

c$.4\mathrm{.}10\%$

d$.6\mathrm{.}20\%$

e$.4\mathrm{.}19\%$