Questions: APY = (1 + 0.0899/12)^12 - 1

Transcript text: $\mathrm{APY}=\left(1+\frac{0.0899}{12}\right)^{12}-1$

Solution

To calculate the Annual Percentage Yield (APY) from a given nominal interest rate compounded monthly, we use the formula:

\[ \text{APY} = \left(1 + \frac{r}{n}\right)^n - 1 \]

where $ r $ is the nominal interest rate and $ n $ is the number of compounding periods per year. In this case, $ r = 0.0899 $ and $ n = 12 $.

Step 1: Given Values

We are given the nominal interest rate $ r = 0.0899 $ and the number of compounding periods per year $ n = 12 $.

Step 2: APY Calculation

Using the formula for Annual Percentage Yield (APY):

\[ \text{APY} = \left(1 + \frac{r}{n}\right)^n - 1 \]

we substitute the values:

\[ \text{APY} = \left(1 + \frac{0.0899}{12}\right)^{12} - 1 \]

Step 3: Compute the Result

Calculating the expression gives us:

\[ \text{APY} \approx 0.0937 \]

Thus, the Annual Percentage Yield (APY) is

\[ \boxed{0.0937} \]

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