APR to APY Calculator

What this calculator does

Two rates can describe the exact same account and still be different numbers. One is the rate on the label. The other is what you actually end up with once compounding has done its work. This calculator turns the first into the second: you give it an APR and how often the interest compounds, and it hands you the APY.

It is a small conversion, but it is the one that lets you compare rates honestly, because a rate is only meaningful once you know how often it compounds.

APR and APY, and what separates them

APR, the annual percentage rate, is the plain stated rate. It is the yearly rate before you account for compounding within the year. APY, the annual percentage yield, is what that rate actually becomes once the interest starts earning interest of its own.

The thing standing between them is compounding frequency. If interest is added only once a year, the APR and the APY are the same. But add it monthly, or daily, and each little chunk of interest starts earning too, so the effective yield creeps above the stated rate. The more often it compounds, the wider that gap grows. That is the whole reason APY exists: it is the honest, compounding-included version of the rate.

A worked example: 7% is not always 7%

Take an APR of 7% and watch what the compounding frequency does to it:

Compounded once a year, 7% stays 7%. Compounded monthly, that same 7% is really 7.229%. Compounded daily, it is 7.250%. Nothing about the stated rate changed. Only the frequency did, and the frequency alone is worth a fifth of a percent here. On a large balance over many years, that difference is real money.

Why you would bother converting

Here is where this earns its place. Savings accounts and CDs are usually advertised as an APY, while loans and credit cards are quoted as an APR. So when you try to compare them directly, you are comparing two rates that are not measured the same way, which is not a fair fight.

Converting an APR to its APY puts everything on the same footing, the effective yearly rate with compounding baked in, so you can line them up honestly. This is not a made-up number either. In the US, the APY is defined in federal law through the Federal Reserve's Regulation DD, precisely so that savers can compare accounts on equal terms. If you want to watch that compounding grow a balance over time, our compound interest calculator does exactly that, and for the borrowing side, where fees also enter the picture, the APR calculator shows the true cost of a loan.

How to use it

• APR. The stated annual percentage rate, entered as a percentage.
• The number of periods. How many times a year the interest compounds: 1 for annually, 4 for quarterly, 12 for monthly, 365 for daily.

Press Calculate and it returns the APY. Press Reset to go back to the starting values.

Questions people ask

What is the difference between APR and APY?

APR is the stated annual rate before compounding within the year. APY is the effective rate after compounding, so it reflects the interest that your interest earns. When interest compounds more than once a year, the APY is higher than the APR.

Why does more frequent compounding raise the APY?

Because each time interest is added, it joins the balance and starts earning interest itself. The more often that happens, the more the yield builds on itself, so a higher compounding frequency produces a higher APY from the same APR.

Which is bigger, APR or APY?

APY is bigger, unless interest compounds only once a year, in which case they are equal. APY can never be lower than the APR it comes from, because compounding only ever adds to the yield.

References

The APY, the effective rate that reflects the stated rate and how often it compounds, is defined in U.S. federal law through the Federal Reserve's Regulation DD. The distinction between a stated interest rate and the annual percentage rate follows the U.S. Consumer Financial Protection Bureau.

1. Board of Governors of the Federal Reserve System. Regulation DD: Truth in Savings (annual percentage yield and compounding). https://www.federalreserve.gov/supervisionreg/regddcg.htm
2. Consumer Financial Protection Bureau. What is the difference between a loan interest rate and the APR? consumerfinance.gov