Answer
$ 5.09\%$
Work Step by Step
The effective interest rate $r_{eff}$ of an investment$\\$
paying a nominal interest rate of $r_{nom}=5\%=0.05 \\\\$
compounded m$=4 \ \ \ \ $ times per year is$\\$
$ r_{eff}=(1+\displaystyle \frac{ r_{nom}}{m})^{m}-1$
$=(1+\frac{ 0.05}{4})^{4}-1\approx$0.0509453369141$\\\\$
Rounded to the nearest $0.01\% $ (4th decimal place):
$ r_{eff}=5.09\%$
