We are given a a savings and loan investment that offers a monthly compounding rate with an annual percentage yield (APY) of 5.25%.
We are now required to use this information to calculate the nominal rate of interest compounded monthly.
The compound interest formula for monthly compounding is given as;
[tex]\begin{gathered} \text{Compound Interest (monthly):} \\ A=P(1+\frac{r}{n})^{tn} \end{gathered}[/tex]
Where the variables are;
[tex]\begin{gathered} A=\text{Amount at the end of the investment period} \\ P=\text{Initial amount invested} \\ r=annual\text{ rate of interest} \\ n=\text{Number of times compounding is done per period} \\ t=\text{time, period of investment (in years)} \end{gathered}[/tex]
However, where we have the annual percentage yield already given, we can use that information to calculate the annual rate of interest as given by the formula below;
[tex]\text{APY}=1(1+\frac{r}{n})^n-1[/tex]
The variables given are;
[tex]\begin{gathered} \text{APY}=5.25\%\text{ OR }0.0525 \\ n=12 \\ r=\text{?} \end{gathered}[/tex]
Substituting these into the formula we now have;
[tex]0.0525=1(1+\frac{r}{12})^{12}-1[/tex]
