APR to APY Calculator

How to Use This Calculator

1. Choose the direction — APR to APY if you have a nominal rate, or APY to APR if you have an effective rate.
2. Enter the rate — the interest rate you want to convert.
3. Pick compounding — how often interest compounds: daily, monthly, quarterly, semi-annually, annually, or continuously.
4. Compare results — the table shows the converted rate for every compounding frequency so you can compare products side by side.

Understanding APR vs APY

Financial institutions use two different ways to express interest rates, and the difference matters more than most people realize.

APR (Annual Percentage Rate) is the simple, nominal rate. If a bank offers 5% APR on a savings account, it means the annual interest rate is 5% — but this doesn't tell you how often interest compounds.

APY (Annual Percentage Yield) is the effective rate after accounting for compounding. With 5% APR compounded monthly, you earn interest on your interest 12 times per year, giving you an APY of 5.1162%. On a $10,000 deposit, that's an extra $11.62 per year compared to simple interest.

The formula to convert APR to APY is: APY = (1 + APR/n)^n - 1, where n is the number of compounding periods per year. The gap between APR and APY grows with higher rates and more frequent compounding.

Banks know this, which is why they advertise APY on savings accounts (it looks higher) and APR on loans (it looks lower). As a consumer, always compare like with like: APY to APY for savings, and APR to APR (including fees) for loans. This calculator makes that conversion instant.

Frequently Asked Questions

What is the difference between APR and APY?

APR (Annual Percentage Rate) is the nominal interest rate without considering compounding. APY (Annual Percentage Yield) is the effective rate after compounding is applied. APY is always equal to or greater than APR. For example, 5% APR compounded monthly equals 5.1162% APY — the extra 0.1162% comes from earning interest on interest throughout the year.

Why does compounding frequency matter?

More frequent compounding means you earn interest on previously earned interest more often, which increases the effective yield. At 5% APR: annual compounding gives 5.0000% APY, monthly gives 5.1162% APY, and daily gives 5.1267% APY. The difference grows with higher rates and longer time periods.

Which rate should I use to compare financial products?

For savings accounts and CDs, compare APY — it shows what you actually earn. For loans and credit cards, compare APR — it shows what you actually pay (though note that loan APR may include fees beyond interest). Banks are required by law to disclose both, but they tend to advertise whichever looks better: APY for savings, APR for loans.

What is continuous compounding?

Continuous compounding is the mathematical limit of compounding infinitely often. Instead of compounding daily (365 times/year), it compounds at every instant. The formula uses the constant e (≈2.71828): APY = e^APR - 1. In practice, the difference between daily and continuous compounding is negligible — at 5% APR, daily gives 5.1267% APY while continuous gives 5.1271% APY.

How do I convert APY back to APR?

To convert APY to APR, use the inverse formula: APR = n × [(1 + APY)^(1/n) - 1], where n is the compounding frequency. This calculator handles both directions — just toggle the conversion mode. This is useful when a bank advertises APY and you want to know the underlying nominal rate for comparison.

Does APR include fees?

It depends on the context. For mortgages and some consumer loans, APR is required by the Truth in Lending Act (TILA) to include certain fees like origination costs, making it higher than the base interest rate. For credit cards and savings accounts, APR typically equals the interest rate without additional fees. Always read the fine print to understand what's included.

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