APY Calculator
Turn a nominal interest rate into the annual percentage yield (APY) you actually earn once compounding is counted. Add a deposit and term to see your final balance and interest earned, or switch to reverse mode to find the nominal rate that hits a target APY.
Formula
Worked example
A 5% nominal rate compounding monthly (n = 12): APY = (1 + 0.05/12)^12 − 1 = 1.05116 − 1 = 0.05116, or about 5.116%. A 10,000 deposit at that APY for one year grows to about 10,511.62, earning 511.62 in interest.
What APY actually measures
Annual percentage yield is the real rate of return you earn over one year once compounding is taken into account. A nominal rate states how much interest is charged per year, but it ignores the fact that interest earned earlier in the year itself starts earning interest. APY folds that effect in, so two accounts quoting different nominal rates and compounding schedules can be compared on equal footing using a single number.
Why compounding frequency matters
For a fixed nominal rate, compounding more often raises the APY because interest is credited and begins compounding sooner. Moving from annual to monthly to daily compounding nudges the yield upward, though with diminishing returns: the jump from annual to monthly is far larger than the jump from daily to continuous. Continuous compounding is the mathematical ceiling, where APY equals e raised to the rate minus one. This is why banks advertise APY rather than the nominal rate, it reflects what a depositor will genuinely earn over a full year.
Projecting a balance and reversing the math
Enter an initial deposit and a term and the calculator grows that money at the APY, reporting the final balance and the interest earned in your chosen currency, since APY is the once-compounded effective rate you can apply year over year. Switch to reverse mode to go the other way: give it a target APY and a compounding frequency, and it solves for the nominal rate a bank would need to quote to deliver that yield. That is useful when an advertised APY is all you have and you want the underlying periodic rate.
APY at a 5% nominal rate by compounding frequency
| Compounding | Periods per year (n) | APY |
|---|---|---|
| Annually | 1 | 5.000% |
| Semi-annually | 2 | 5.062% |
| Quarterly | 4 | 5.095% |
| Monthly | 12 | 5.116% |
| Daily | 365 | 5.127% |
| Continuously | ∞ | 5.127% |
How often interest compounds changes the effective annual yield.
Frequently asked questions
What is the difference between APY and the nominal interest rate?
The nominal rate is the stated annual rate before compounding. APY is the effective annual return after compounding is applied, so APY is always equal to or higher than the nominal rate whenever interest compounds more than once a year.
How is APY different from APR?
APY accounts for compounding and is used for what you earn on savings and investments. APR typically describes borrowing costs and does not compound the periodic rate, so for the same nominal rate APY will be higher than APR.
Why does daily compounding barely beat monthly?
Compounding gains follow a curve with diminishing returns. Most of the benefit comes from compounding several times a year; going from monthly to daily adds only a tiny fraction of a percentage point because the periods are already small, and continuous compounding is the ceiling.
How do I find the nominal rate from an advertised APY?
Switch the calculator to reverse mode, enter the APY and how often the account compounds, and it solves the formula backward: nominal rate equals n times the n-th root of (1 + APY) minus one. For continuous compounding it uses the natural log of (1 + APY).
How much will my deposit earn at this APY?
Enter your initial deposit and the term in years. Because APY is the effective once-yearly rate, the final balance is the deposit times (1 + APY) raised to the number of years, and the interest earned is the difference between that final balance and your deposit.