APR to APY Calculator

How to Convert Between APR and APY

Understanding the relationship between Annual Percentage Rate (APR) and Annual Percentage Yield (APY) is crucial for accurately comparing different financial products. This calculator helps you convert between these two measures of interest rates.

Conversion Formulas

The formulas for converting between APR and APY are:

APR to APY:

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

APY to APR:

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

Where:

• APR = Annual Percentage Rate
• APY = Annual Percentage Yield
• n = Number of compounding periods per year

Calculation Steps

1. Determine whether you're converting from APR to APY or vice versa.
2. Input the known rate (either APR or APY).
3. Select the compounding frequency.
4. Apply the appropriate formula to calculate the result.

Example Calculation

Let's convert an APR of 5% to APY, compounded monthly:

Given:

• APR = 5% = 0.05
• n = 12 (monthly compounding)

Using the APR to APY 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 APR of 5% compounded monthly is equivalent to an APY of 5.12%.

Visual Representation

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