APR to APY Converter - Annual Percentage Rate vs Yield

How to use this tool

1. Select the direction of conversion: APR -> APY or APY -> APR.
2. Type a rate from 0% to 99.99%, or explore rates with the slider.
3. Choose a compounding frequency, including continuous compounding.
4. Optionally enter a balance to estimate interest and the ending balance after one year.
5. The converted rate and frequency comparison are shown instantly.

APR vs APY: stated rate and effective yield

This converter compares a nominal annual rate (APR) with its effective annual yield (APY) under a chosen compounding convention. APR is the rate before intra-year compounding; APY accounts for interest being added during the year. For savings, a bank may quote APY so customers can compare the yield across accounts with different compounding schedules. This calculator uses the same convention for borrowing examples, but it does not include loan fees.

For discrete compounding, divide the nominal annual rate by the number of periods, add one, then raise that amount to the number of periods. For example, a 5% APR compounded monthly gives an APY of about 5.1162%. The reverse calculation solves for the nominal rate that produces the entered effective yield at that frequency.

APY = (1 + APR/n)ⁿ − 1
APR = n × ((1 + APY)^(1/n) − 1)
where n = compounding periods per year

Continuous compounding

Continuous compounding is the mathematical limit as the compounding periods become infinitely frequent. It uses APY = e^APR − 1 in the forward direction and APR = ln(1 + APY) in reverse. Most consumer accounts do not compound continuously; daily compounding is already very close at ordinary rates. For example, a continuous 5% APR produces a 5.1271% APY.

How frequency changes the effective yield

More frequent compounding produces a larger effective annual yield when the same nonnegative nominal rate is held fixed. The difference can be small at moderate rates, but it grows as the nominal rate rises. The live comparison table includes common schedules and the continuous limit so you can compare their effect using the same input.

Estimate one year of interest

Entering an optional principal or balance shows the interest and ending balance for one year. In APR-to-APY mode, the estimate uses the converted effective APY. In APY-to-APR mode, it uses the APY you entered, since that is the effective annual yield. For example, $10,000 at 5% APR compounded monthly earns about $511.62, for an ending balance of $10,511.62. This is a simple one-year estimate assuming the rate stays fixed and there are no additional deposits, withdrawals, or fees; it is not a multi-year projection.

When each number matters

For savings accounts and certificates of deposit, APY is useful for comparing the annual yield when balances and account terms are otherwise similar. For credit cards, the issuer may quote a nominal APR while interest accrues daily. A 24.99% APR compounded daily converts to a 28.3787% effective annual yield under this formula. Actual card interest depends on the balance, payments, grace period, and issuer terms, so this conversion is not a payoff quote.