A bank features a savings account that has an annual percentage rate of r=3.2%. Find the Annual Percentage Yield (APY) for the savings account if the interest is compounded according to the following schedules:


To find the **Annual Percentage Yield (APY)** for a savings account based on different compounding schedules, we use the following formula:

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

Where:
- \(r\) is the annual interest rate (expressed as a decimal).
- \(n\) is the number of compounding periods per year.

The given interest rate is \(r = 3.2\% = 0.032\).

### Let’s calculate the APY for different compounding schedules:

#### 1. **Compounded Annually** (\(n = 1\)):
\[
APY = \left(1 + \frac{0.032}{1}\right)^1 - 1 = 0.032 \text{ or } 3.2\%
\]

#### 2. **Compounded Semi-Annually** (\(n = 2\)):
\[
APY = \left(1 + \frac{0.032}{2}\right)^2 - 1 = \left(1 + 0.016\right)^2 - 1 = 1.032256 - 1 = 0.032256 \text{ or } 3.2256\%
\]

#### 3. **Compounded Quarterly** (\(n = 4\)):
\[
APY = \left(1 + \frac{0.032}{4}\right)^4 - 1 = \left(1 + 0.008\right)^4 - 1 = 1.032328 - 1 = 0.032328 \text{ or } 3.2328\%
\]

#### 4. **Compounded Monthly** (\(n = 12\)):
\[
APY = \left(1 + \frac{0.032}{12}\right)^{12} - 1 = \left(1 + 0.0026667\right)^{12} - 1 = 1.032445 - 1 = 0.032445 \text{ or } 3.2445\%
\]

#### 5. **Compounded Daily** (\(n = 365\)):
\[
APY = \left(1 + \frac{0.032}{365}\right)^{365} - 1 = \left(1 + 0.00008767\right)^{365} - 1 = 1.032488 - 1 = 0.032488 \text{ or } 3.2488\%
\]

### Summary of APYs:

- **Annually**: 3.2%
- **Semi-Annually**: 3.2256%
- **Quarterly**: 3.2328%
- **Monthly**: 3.2445%
- **Daily**: 3.2488%

Would you like a more detailed explanation of how each compounding schedule affects the APY?

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Here are 5 related questions you can explore:
1. What is the difference between APR and APY in banking?
2. How does compounding frequency affect the growth of savings?
3. How can you use APY to compare different savings accounts?
4. What happens if interest is compounded continuously?
5. How can you estimate future savings using APY?

**Tip**: The more frequently interest is compounded, the higher the APY, leading to slightly higher returns!

A bank features a savings account that has an annual percentage rate of r=3.2%. Find the Annual Percentage Yield (APY) for the savings account if the interest is compounded according to the following schedules:

Learn how to calculate the Annual Percentage Yield (APY) for a savings account with a 3.2% APR. Explore how different compounding schedules (annually, semi-annually, quarterly, monthly, and daily) affect the APY with step-by-step calculations.

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