APY Calculator

The interest rate - the nominal rate - is what the bank states before compounding is taken into account. APY is what you actually receive over a year once compounding is applied. APY is therefore always equal to or higher than the nominal rate, and the gap widens as compounding gets more frequent or the rate rises.

The spread from annual to daily compounding is about $12.70 a year on $10,000 - small, but it is free money and APY lets you capture it in a single comparison figure without doing the arithmetic yourself.

Note. This is why APY exists. Comparing two products by their nominal rates is only valid if both compound at the same frequency. APY neutralises that difference.

• r - the nominal annual rate as a decimal, so 5% becomes 0.05.
• n - the number of compounding periods per year. Monthly is 12, daily is 365.
• APY - returned as a decimal; multiply by 100 for a percentage.

The expression (1 + r/n) is the growth over one period. Raising it to the power n repeats that growth n times across the year. Subtracting 1 isolates the growth from the starting balance itself.

Reversing the calculation - finding the nominal rate that produces a target APY - is just as useful when a bank advertises the yield but you need the formula input. Enter the APY you were quoted with n set to 1 and you can project growth directly, because the compounding is already inside the figure.

Account A advertises 4.85% compounded monthly. Account B advertises 4.78% compounded daily. Which earns more on $25,000?

Account A wins despite Account B compounding more often, because the higher nominal rate more than offsets the extra frequency. Frequency alone rarely decides the winner - the headline rate usually dominates. But the margin is narrow enough that a difference in fees could reverse it, which is why APY should be compared after fees rather than before.

• Savings accounts, money market accounts and certificates of deposit quote APY in the United States, by regulation. It is the yield you receive.
• Interest-bearing checking accounts quote APY, but the balance is often low enough that the difference is negligible in cash terms.
• Loans and credit cards quote APR, not APY, under the Truth in Lending Act. APR generally excludes the effect of compounding, which makes it a lower number than the equivalent APY would be. This asymmetry is deliberate: it makes borrowing look cheaper and saving look better.
• Investment returns are not APY. A fund quoting an annualised return is describing past performance, not a guaranteed compounding rate.
• Foreign products may use AER or effective rate, which are equivalent concepts under different names.

Note. When a savings product quotes an "interest rate" rather than APY, ask which one it is. If it is a nominal rate, your actual yield will be higher once compounding is applied. If it is already an APY, applying compounding again in this calculator will overstate the result.

At low rates, the difference between nominal rate and APY is almost invisible. At high rates it becomes material.

Below about 2%, daily compounding adds less than a hundredth of a percentage point - the difference between products in that range is noise, and fees or minimum balance requirements will dominate. Above 8%, compounding adds real money and should be part of the comparison.

Note. This calculator assumes compounding across a full year with no deposits or withdrawals. Interest that is paid out rather than reinvested does not compound, and on some accounts interest is only credited monthly or at maturity - in which case the realised APY will fall short of the quoted figure.