Suppose the real risk$-$free rate is $2\mathrm{.}50\%$ and the future rate of inflation is expected to be constant at $2\mathrm{.}90\%.$ What rate of return would you expect on a $5-$year Treasury security, assuming the pure expectations theory is valid? Disregard cross$-$product terms, i$.$e$.,$ if averaging is required, use the arithmetic average.

$$ a$.5\mathrm{.}40\%$

$$ b$.6\mathrm{.}32\%$

$$ c$.6\mathrm{.}05\%$

$$ d$.4\mathrm{.}64\%$

$$ e$.5\mathrm{.}45\%$