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

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

$($b$)$ Compute the effective interest rate corresponding to a nominal interest rate of $12\mathrm{.}87\%$ compounded monthly.

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

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

$13\%$ compounded quarterly

$12\mathrm{.}87\%$ compounded monthly