APY, or annual percentage yield, tells you the real rate of return your savings account earns over a year after accounting for compound interest. The formula is straightforward: APY = (1 + i/n)^n − 1, where “i” is the stated interest rate and “n” is the number of times interest compounds per year. Once you understand those two variables, you can calculate APY for any account in seconds.
What APY Actually Measures
Every savings account has a base interest rate, sometimes called the nominal or stated rate. That rate is a simple percentage that doesn’t reflect how often your interest gets added back to your balance. APY fills that gap. It captures the total return you’d earn in a year by factoring in compounding, the process where interest you’ve already earned starts earning its own interest.
Because APY bakes in compounding, it will always be equal to or slightly higher than the stated interest rate. The more frequently interest compounds, the wider the gap between the two numbers. That’s why APY is the standard comparison tool when you’re shopping for a savings account: it gives you an apples-to-apples view of what each account will actually pay you.
The APY Formula
Here’s the formula most commonly used:
APY = (1 + i / n)n − 1
- i = the annual interest rate, expressed as a decimal (so 4.5% becomes 0.045)
- n = the number of compounding periods per year (365 for daily, 12 for monthly, 4 for quarterly)
The result is a decimal you multiply by 100 to get a percentage. That percentage is your APY.
Step-by-Step Calculation
Suppose your savings account has a stated interest rate of 5% and compounds interest daily. Here’s how to work through it:
First, convert the interest rate to a decimal: 5% ÷ 100 = 0.05. Next, divide by the number of compounding periods: 0.05 ÷ 365 = 0.00013699. Add 1 to get 1.00013699. Raise that to the power of 365 (the number of compounding periods): 1.00013699365 = 1.05127. Finally, subtract 1: 1.05127 − 1 = 0.05127. Multiply by 100 and you get an APY of about 5.13%.
That extra 0.13% over the stated 5% rate is the effect of daily compounding. On a $10,000 balance, it means you’d earn roughly $513 over a year instead of $500. The gap grows larger with bigger balances and higher interest rates.
How Compounding Frequency Changes APY
The same stated interest rate produces a different APY depending on how often your bank compounds. Using 5% as the base rate, here’s what happens at common intervals:
- Annually (n = 1): APY = 5.00%. Compounding once a year means the APY and the stated rate are identical.
- Quarterly (n = 4): APY = 5.09%. Interest is calculated and added to your balance four times a year.
- Monthly (n = 12): APY = 5.12%. Each month’s interest earns interest for the remaining months.
- Daily (n = 365): APY = 5.13%. Interest accrues every day, producing the highest yield of the four.
The jump from annual to daily compounding on a 5% rate is about 0.13 percentage points. That sounds tiny, but it compounds itself over time. On a $50,000 balance held for five years, that difference adds up to roughly $350 in extra earnings with no additional effort on your part. Most online savings accounts compound daily, which is one reason their advertised APYs tend to edge out accounts that compound monthly or quarterly.
The CFPB’s Official Formula
The Consumer Financial Protection Bureau, which enforces federal savings-account disclosure rules, uses a slightly different version of the formula in its regulations:
APY = 100 × [(1 + Interest / Principal)(365 / Days in term) − 1]
In this version, “Interest” is the total dollar amount of interest earned, “Principal” is the amount deposited at the start, and “Days in term” is how long the account was open. This approach works backward from actual dollars earned rather than forward from a stated rate. Banks use it to verify that the APY they advertise matches the interest they actually pay. You’d use it if you wanted to check your own account: take the interest you received, divide by your starting balance, and plug in the number of days.
For example, if you deposited $10,000, earned $256 in interest over 183 days, the math would be: (1 + 256/10,000)(365/183) − 1 = 0.0520, or 5.20% APY. This lets you confirm whether your bank’s stated APY lines up with the interest that actually hit your account.
Why the Advertised APY May Not Match Your Earnings
The APY your bank advertises assumes you deposit money on day one and leave it untouched for a full year. In practice, most people add or withdraw funds throughout the year, which changes the effective return. If you pull half your balance out in June, your total interest will be lower than the APY implied, not because the rate was wrong but because your average balance was smaller.
Some savings accounts also use tiered interest rates, paying one rate on the first portion of your balance and a different rate on amounts above a certain threshold. In that case, the bank calculates a blended APY using the total interest earned across all tiers divided by your full principal. The advertised APY for each tier reflects what you’d earn if your entire balance sat within that tier, so the yield you actually experience may land somewhere in between.
Variable-rate accounts add another wrinkle. Most savings accounts can change their rate at any time. The APY you see today is a snapshot, not a guarantee for the full year. If rates drop mid-year, your actual earnings will trail the APY you saw when you opened the account.
Quick Way to Estimate Without the Formula
If you don’t want to pull out a calculator, a shortcut gets you close. Take the stated interest rate and divide it by 100, then divide that by 2 and multiply by the same rate. Add the result to the original rate. For a 5% rate: (0.05 × 0.05) / 2 = 0.00125, so the APY is approximately 5% + 0.125% = 5.125%. That’s within a hair of the exact daily-compounding answer of 5.13%.
This shortcut works well for rates under about 10%. Above that, the approximation drifts further from the real number, and you’re better off using the full formula or an online APY calculator.