APY Calculator
The annual percentage yield is what a deposit account actually returns in a year once compounding is counted. Comparing two accounts by their headline rates instead of their APYs is the most common way savers pick the slower one.
Annual percentage yield (APY)
5.12%
- Balance after one year
- $10,511.62
- Interest earned in one year
- $511.62
- Continuous-compounding ceiling
- 5.13%
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
APY = (1 + r/n)^n - 1
- APY
- Annual percentage yield — the effective annual return
- r
- Nominal annual rate as a decimal (APR)
- n
- Number of compounding periods per year
- e
- Euler's number, about 2.71828, used for continuous compounding
How to check the result by hand
- 1
Find the nominal rate and the compounding frequency
Both are in the account agreement or disclosure. The rate alone is not enough — a 5% rate compounds differently if credited annually, monthly or daily.
- 2
Convert the percentage to a decimal
Divide by 100. A 5% nominal rate becomes 0.05. Leaving it as 5 produces a nonsense APY above one hundred thousand percent.
- 3
Divide the rate by the number of periods
Monthly compounding means twelve periods: 0.05 / 12 = 0.00416667. This is the periodic rate actually applied each time interest is credited.
- 4
Add one, raise to the nth power, subtract one
(1 + 0.00416667)^12 = 1.0511619, so the APY is 0.0511619. Expressed as a percentage that is 5.11619%. The exponent is doing all the compounding work.
- 5
Apply it to the deposit
Multiply principal by (1 + APY). For $10,000 at 5.11619%, the year ends at $10,511.62 — compared with $10,500.00 if the same 5% had compounded annually.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate APY page.