$($a$)$ Compute the effective interest rate corresponding to a nominal interest rate of $13\%$ compounded semiannually.

Effective interest rate, as a percent, rounded to $4$ decimal places $=$

$\%$

$($b$)$ Compute the effective interest rate corresponding to a nominal interest rate of $12\mathrm{.}74\%$ compounded monthly.

Effective interest rate, as a percent, rounded to $4$ decimal places $=$

$($c$)$ Select the investment that offers the better return.

$13\%$ compounded semiannually

$12\mathrm{.}74\%$ compounded monthly