We have the formula to calculate the annual percentage yield that let us compare different investment or interest rates with different capitalization periods, transforming them in a consistent annual measure.
The formula is:
[tex]\text{APY}=(1+\frac{r}{n})^n-1[/tex]
where r: nominal annual interest rate and n: subperiod of capitalization (number of capitalizations in a year).
In this case, with an interest rate of 3% (r=0.03) monthly compounded (n=12) we can calculate the APY as:
[tex]\begin{gathered} \text{APY}=(1+\frac{r}{n})^n-1 \\ \text{APY}=(1+\frac{0.03}{12})^{12}-1 \\ \text{APY}=(1+0.0025)^{12}-1 \\ \text{APY}=1.0025^{12}-1 \\ \text{APY}\approx1.0304-1 \\ \text{APY}\approx0.0304 \\ \text{APY}\approx3.04\% \end{gathered}[/tex]
Answer: the APY for this investment is 3.04%.
