APR to APY Converter

The True Cost of Money: APR vs. APY

When shopping for a loan or a savings account, you will often encounter two different acronyms: APR (Annual Percentage Rate) and APY (Annual Percentage Yield). While they both express interest rates, the difference between them can mean hundreds or thousands of dollars over time. Our calculator helps you convert APR to APY, revealing the true effect of compound interest.

What is APR?

Annual Percentage Rate (APR) is the simple annual interest rate.
- It represents the cost of borrowing money or the return on an investment without taking compounding into account.
- Lenders often advertise loans in APR because it looks lower (more attractive for borrowers).
- It essentially answers: "What is the flat rate I am paying per year?"

What is APY?

Annual Percentage Yield (APY), also known as the Effective Annual Rate (EAR), takes into account the frequency of compounding.
- Compounding puts interest on top of previously earned interest.
- Banks advertise savings accounts in APY because it looks higher (more attractive for savers).
- It essentially answers: "What will I actually earn or pay by the end of the year if interest is reinvested?"

The Conversion Formula

To convert APR to APY, use the following formula:

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

Where:
- APR is the annual rate (expressed as a decimal, e.g., 5% = 0.05).
- n is the number of compounding periods per year.

Common Compounding Frequencies (n):
- Monthly: 12
- Quarterly: 4
- Daily: 365 (most credit cards compound daily)

Why It Matters

Imagine a credit card with an APR of 20%. If it compounds daily (n=365):
$$ APY = \left(1 + \frac{0.20}{365}\right)^{365} - 1 \approx 0.2213 $$
The effective rate (APY) is actually 22.13%. This 2% difference is the "hidden" cost of compounding that borrowers often overlook.

Key Takeaways

1. Borrowers: Focus on the APY to see the real cost of debt.
2. Savers: Focus on the APY to see the real growth of savings.
3. Frequency Matters: The more frequently interest compounds, the higher the APY will be relative to the APR.