calculate the apy for an account that pays 9%: 1. compounded daily 2. compounded monthly 3. compounded…

Explanation:

Step1: Recall the APY formula

The formula for APY is $APY=(1 + \frac{r}{n})^{n}-1$, where $r$ is the annual interest rate (in decimal form) and $n$ is the number of compounding periods per year. Given $r = 0.09$.

Step2: Calculate APY for daily - compounding

For daily - compounding, $n = 365$. So, $APY=(1+\frac{0.09}{365})^{365}-1$. $APY=(1 + 0.000246575)^{365}-1$. $APY=(1.000246575)^{365}-1$. $APY\approx1.09416 - 1=0.09416$ or $9.416%$.

Step3: Calculate APY for monthly - compounding

For monthly - compounding, $n = 12$. So, $APY=(1+\frac{0.09}{12})^{12}-1$. $APY=(1 + 0.0075)^{12}-1$. Using the formula $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$, or simply calculating $(1.0075)^{12}\approx1.09381$. $APY\approx1.09381-1 = 0.09381$ or $9.381%$.

Step4: Calculate APY for annual - compounding

For annual - compounding, $n = 1$. So, $APY=(1+\frac{0.09}{1})^{1}-1$. $APY=(1 + 0.09)-1=0.09$ or $9%$.

Answer:

1. $9.416$
2. $9.381$
3. $9$