APR to APY Calculator
Enter a nominal rate (APR) and how often interest is added to see the effective annual rate (APY), or go the other way from an APY to the APR. A table shows the result for every compounding frequency, from yearly to continuous, and you can add a starting balance and a number of years to see what it grows to. Everything runs in your browser.
| Compounding | APR | APY |
|---|---|---|
| Annually (1 a year) | 5.0000% | 5.0000% |
| Semiannually (2 a year) | 5.0000% | 5.0625% |
| Quarterly (4 a year) | 5.0000% | 5.0945% |
| Monthly (12 a year) | 5.0000% | 5.1162% |
| Weekly (52 a year) | 5.0000% | 5.1246% |
| Daily (365 a year) | 5.0000% | 5.1267% |
| Continuously | 5.0000% | 5.1271% |
APR is the stated yearly rate, and APY (also called EAR) is what you actually earn or pay in a year once the interest itself earns interest. For a rate r compounded n times a year, APY = (1 + r / n)^n - 1, and for continuous compounding it is e^r - 1. The more often interest is added, the higher the APY, but the gain shrinks quickly: 5% compounded monthly is 5.12%, and compounded continuously it is 5.13%. Many U.S. credit cards quote a nominal APR compounded monthly, so their true yearly cost is higher than the APR. Everything is worked out in your browser and nothing is uploaded.
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Math & MoneyAbout the APR to APY Calculator
APR is the stated yearly rate, and APY, also called the effective annual rate or EAR, is what you actually earn or pay in a year once interest starts earning interest. For a rate r compounded n times a year, APY = (1 + r / n)^n - 1. A 5 percent APR compounded monthly gives 5.1162 percent, compounded daily it gives 5.1267 percent, and compounded continuously it gives e^0.05 - 1, which is 5.1271 percent. The more often interest is added, the higher the APY, but the gain gets smaller each time, and it stops at the continuous limit. Going the other way, the nominal rate that gives a target APY at n periods is n times ((1 + APY)^(1 / n) - 1). Many U.S. credit cards quote a nominal APR that compounds monthly, so a 22.99 percent APR costs about 25.57 percent over a year, and 29.99 percent costs about 34.48 percent. Savings accounts usually quote APY directly. The balance estimate applies the nominal rate and the compounding to the starting amount with no deposits or withdrawals. The calculations use log and exponent functions that keep tiny rates accurate. Nothing is uploaded.
What is the difference between APR and APY?▾
APR is the nominal yearly rate before compounding is counted. APY is the effective rate after it. They are equal only when interest is added once a year. With monthly compounding a 5 percent APR is a 5.1162 percent APY.
How do I convert APR to APY?▾
Use APY = (1 + APR / n)^n - 1, where n is the number of compounding periods in a year. For 12 percent compounded monthly, (1.01)^12 - 1 is 12.68 percent. The tool does this for every frequency at once.
How do I convert APY to APR?▾
Reverse the formula: APR = n x ((1 + APY)^(1 / n) - 1). For a 5.1162 percent APY with monthly compounding, the nominal rate is 5 percent. Switch the direction tab to APY to APR to do it.
Why does a credit card cost more than its APR?▾
Because the interest is added to the balance every month and then earns interest itself. A card quoted at 22.99 percent APR with monthly compounding has an effective annual rate of about 25.57 percent if the balance is carried all year.
Does more frequent compounding help a lot?▾
Only a little. At 5 percent, going from yearly to monthly adds 0.12 points, and from monthly to daily adds about 0.01 more. Continuous compounding is the upper limit. Nothing you enter is uploaded.