APY Calculator

How to Calculate APY

Annual Percentage Yield (APY) is a standardized measure that represents the effective annual rate of return on an investment or savings account, taking into account the effect of compound interest. Here's how to calculate and understand APY:

APY Formula

The formula for calculating APY is:

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

Where:

• APY = Annual Percentage Yield
• r = Annual interest rate (in decimal form)
• n = Number of times interest is compounded per year

Calculation Steps

1. Convert the annual interest rate to decimal form (divide by 100).
2. Determine the compounding frequency (n).
3. Add 1 to the result of the interest rate divided by n.
4. Raise this sum to the power of n.
5. Subtract 1 from the result.
6. Convert the final result to a percentage by multiplying by 100.

Example Calculation

Let's calculate the APY for an account with a 5% annual interest rate, compounded monthly:

Given:

• Annual interest rate (r) = 5% = 0.05
• Compounding frequency (n) = 12 (monthly)

Applying the formula:

$$\text{APY} = \left(1 + \frac{0.05}{12}\right)^{12} - 1$$

$$\text{APY} = (1 + 0.004167)^{12} - 1$$

$$\text{APY} = 1.0512 - 1 = 0.0512$$

$$\text{APY} = 5.12\%$$

Therefore, an account with a 5% annual interest rate compounded monthly has an APY of 5.12%.

Visual Representation

This diagram illustrates the difference between the stated interest rate and the APY. The green bar represents the annual interest rate of 5%, while the blue bar shows the calculated APY of 5.12%. The slight increase in height of the APY bar demonstrates the effect of compound interest.