Assume that the real risk$-$free rate is expected to remain constant at $2$ percent per year and that inflation is expected to be $5$ percent this coming year $($Year $1),$ jump to $7$ percent next year $($Year $2),$ and decrease to $4$ percent for all years after $($Year $3,4,5,$ etc.$).$ Assuming that the expectations theory is correct, determine the nominal annual interest rate on $5-$year, riskfree securities today $($Year $0).$

$6\mathrm{.}800\%$

$7\mathrm{.}333\%$

$6\mathrm{.}571\%$

$6\mathrm{.}667\%$

$7\mathrm{.}000\%$