# Free online APY calculator

> APY (Annual Percentage Yield) is the effective annual return after accounting for compounding. This calculator converts a nominal rate into APY for every compounding frequency so.

Convert a nominal interest rate to Annual Percentage Yield (APY) for any compounding frequency — daily, weekly, monthly, quarterly, semiannual, annual, or continuous.

**Interactive version:** https://onlinecalculator.me/finance/apy/
**Category:** Finance

## How to use

1. Enter the nominal annual rate — the percentage listed on the account or loan offer.
2. Select the compounding frequency that matches the account.
3. The calculator instantly shows the APY and a comparison table for all seven frequencies.

## The formula

For discrete compounding:

```
APY = (1 + r / n)^n − 1
```

Where `r` is the nominal rate as a decimal and `n` is the number of compounding periods per year (daily = 365, weekly = 52, monthly = 12, quarterly = 4, semiannual = 2, annual = 1).

For continuous compounding:

```
APY = e^r − 1
```

## Worked example

Nominal rate: 5%, compounded monthly:

- `n = 12`, `r = 0.05`
- APY = (1 + 0.05/12)^12 − 1 ≈ **5.1162%**

The same 5% compounded daily yields **5.1267%** — a meaningful difference at scale over many years.

## Notes

- Banks in the US are required to disclose APY under the Truth in Savings Act (Regulation DD).
- When comparing savings accounts, use APY, not the nominal rate. When comparing loans, use APR.
- This calculator uses a 365-day year for daily compounding.

## Frequently asked questions

### What is the difference between APY and APR?

APR (Annual Percentage Rate) is typically used for loans and reflects the cost of borrowing. APY is used for savings and investments and reflects how much you actually earn after compounding. A savings account advertised at 5% APY already accounts for how often interest compounds.

### Why does compounding frequency matter?

Each time interest is added to your balance, it starts earning interest itself. The more often that happens, the faster your money grows. At 5% nominal, daily compounding yields 5.1267% APY versus 5.0% for annual compounding.

### What is continuous compounding?

Continuous compounding is the mathematical limit of compounding infinitely often. The formula is APY = e^r − 1, where e ≈ 2.71828. It produces slightly more than daily compounding and is used in theoretical finance.

### How do I compare two savings accounts with different rates and frequencies?

Convert both to APY. A 5.3% APY account beats a 5.2% nominal rate compounded annually (which is just 5.2% APY). Always compare APY to APY.

## Sources

- [Annual percentage yield — compounding formula](https://en.wikipedia.org/wiki/Annual_percentage_yield) — Wikipedia
- [Appendix A to Part 1030 — Annual Percentage Yield Calculation (Regulation DD)](https://www.consumerfinance.gov/rules-policy/regulations/1030/a/) — Consumer Financial Protection Bureau

## Related calculators

- [Compound interest calculator](https://onlinecalculator.me/finance/compound-interest/) — See how a balance grows over time with any compounding frequency.
- [Savings goal calculator](https://onlinecalculator.me/finance/savings-goal/) — Find out how long it takes or how much to save monthly to hit a target.
- [Investment return calculator](https://onlinecalculator.me/finance/investment-return/) — Calculate ROI and annualized return on any investment.
- [APR calculator](https://onlinecalculator.me/finance/apr/) — The loan-side equivalent — find the true annualized cost of borrowing.

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