APY Calculator

What is APY?

APY stands for annual percentage yield. It is the amount a deposit earns over one year, as a percentage of the balance, once interest is allowed to compound. Because interest credited in one period earns interest in the next, the yield is always at least as high as the stated rate, and higher whenever interest is credited more than once a year.

The stated rate, often called the nominal rate or APR, ignores that effect. APY is the figure to use when you want to compare savings accounts, certificates of deposit or money-market accounts that pay interest on different schedules.

How to use the APY calculator

1. Type the annual interest rate exactly as the bank quotes it, for example 4.25 for 4.25%.
2. Choose the compound frequency: annually, semiannually, quarterly, monthly or daily.
3. Optionally enter an initial balance to see how much it earns.
4. Enter the deposit term and its unit: years, half-years, quarters, months or days.

The first result is always the APY. With a balance entered, you also get the value at the end of the term, the interest accrued and the capital growth. Interest is paid only for complete compounding periods, so a term shorter than one period shows the APY alone. The rate and the term both have to be greater than zero.

The APY formula

APY = (1 + r ÷ n)ⁿ − 1r is the nominal annual rate as a decimal and n is the number of compounding periods in a year.

Going the other way, if you know the yield and want the nominal rate that produces it, solve for r:

r = n × ((1 + APY)^{1 ÷ n} − 1)

For example, a 5% APY on an account that compounds monthly corresponds to a nominal rate of 12 × (1.05^1/12 − 1) = 4.889%. With daily compounding this calculator treats a year as 365.2421 days, which keeps the result consistent with the way terms given in days are converted.

APR versus APY

A lower APR can beat a higher one if it compounds more often. Compare two accounts: Account A quotes 4.80% compounded daily and Account B quotes 4.85% compounded annually. Account B has the bigger headline number, but its APY is 4.850% while Account A's is 4.917%, so Account A pays more.

The gap between the two measures grows with the rate. For monthly compounding:

Effect of the compounding frequency

For a nominal rate of 5%, the yield rises with the number of compounding periods but flattens quickly:

There is a ceiling. Even if interest were credited continuously, 5% could never yield more than e^0.05 − 1 = 5.1271%, only a hair above daily compounding.

Worked example

You deposit $10,000 at 5% compounded monthly and leave it for 3 years. The monthly rate is 0.05 ÷ 12 = 0.0041667, and there are 36 periods.

• APY = (1 + 0.0041667)¹² − 1 = 5.116%.
• Final balance = 10,000 × (1.0041667)³⁶ = $11,614.72.
• Interest accrued = 11,614.72 − 10,000 = $1,614.72, which is a capital growth of 16.147%.

Notice that 16.147% is slightly more than three years of simple 5% would give (15%), because each year's interest starts earning its own interest.

What APY does not tell you

• It assumes the rate stays the same and that interest is left in the account. Variable-rate accounts and promotional rates change the real outcome.
• Fees and minimum balances are not part of the calculation. A monthly maintenance fee can wipe out a small yield advantage.
• Tax and inflation reduce what you keep and what the money can buy. The CD calculator can include both.

In the United States, deposit institutions are required to disclose APY on savings products under the Truth in Savings Act, which is why it is the standard way to compare them. To model regular deposits on top of a balance, use the compound interest calculator.

APY results are estimates for comparison. They are not financial advice, and an institution's own disclosures take precedence. See the disclaimer.