A deposit of $100$ is invested in an account for $10$ years. It earns a constant force of interest of $4\%$ in the first $3$ years, an annual effective rate of discount of $4\%$ during the next $5$ years, and an annual simple interest rate of $4\%$ during the remaining years.

Determine the annual effective interest rate earned over the $10-$year period that results in the same ending account balance as these given rates.

Possible Answers

$4\mathrm{.}00\%$

$4\mathrm{.}09\%$

$4\mathrm{.}16\%$

$4\mathrm{.}84\%$

$4\mathrm{.}92\%$