Answer
5.25%
Work Step by Step
In order to compute the effective annual yield when interest is compounded monthly following formula can be used where Y is the effective yield, r is the rate that is 5% and n is compounding period. The interest is compounded monthly therefore n (compounding period) is taken as 12. By using formula
\[\begin{align}
& Y={{\left( 1+\frac{r}{n} \right)}^{n}}-1 \\
& ={{\left( 1+\frac{0.05}{12} \right)}^{12}}-1 \\
& ={{\left( 1+0.004167 \right)}^{12}}-1
\end{align}\]
\[\begin{align}
& ={{\left( 1.004167 \right)}^{12}}-1 \\
& =1.0512-1 \\
& =0.0512\text{or5}\text{.12}percent
\end{align}\]
Now computing effective annual yield when rate of interest is 5.25% The interest is compounded quarterly therefore, n (compounding period) is taken as 4.
\[\begin{align}
& Y={{\left( 1+\frac{r}{n} \right)}^{n}}-1 \\
& ={{\left( 1+\frac{0.0525}{4} \right)}^{4}}-1 \\
& ={{\left( 1+0.013125 \right)}^{4}}-1
\end{align}\]
\[\begin{align}
& ={{\left( 1.013125 \right)}^{4}}-1 \\
& =1.0535-1 \\
& =0.0535or5.35percent
\end{align}\]
Thus, 5.25% compounded quarterly is the better investment.
