Question

ABC Bank offers a savings account of 4.5% compounded quarterly. Find the APY the bank’s savings account offers

Answer 1

$\bf ~~~~~~~~~~~~ \textit{Annual Yield Formula} \\\\ ~~~~~~~~~~~~ \left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.5\%\to \frac{4.5}{100}\to &0.045\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4 \end{cases} \\\\\\ \left(1+\frac{0.045}{4}\right)^{4}-1\implies 1.01125^4-1~~\approx~~ 0.045765 \\\\\\ 0.045765\cdot 100~~\approx~~ \stackrel{\%}{4.58}$