# APY Calculator

- **URL:** https://codeasystem.com/calculators/finance/apy-calculator/
- **Category:** finance
- **Description:** Convert a nominal interest rate (APR) into the effective annual yield (APY) for any compounding frequency.
- **Primary output:** Effective annual yield (APY): 5.12%

## Inputs
- Nominal rate (APR) (name: `rate`, type: number, example: 5)
- Compounding frequency (name: `compounding`, type: select)

## Outputs
- Effective annual yield (APY): 5.12%
- Nominal rate (APR): 5%

## Formula / methodology
```
APY = (1 + APR/m)^m − 1
```

Nominal rates quote a yearly figure without acknowledging intra-year compounding. APY applies the compounding explicitly: split the nominal rate across m periods per year, compound, and measure the true yearly growth.

## Assumptions & limitations
- Rate stays constant through the year.
- Interest reinvests immediately at the same rate.
- No fees or promotional tiers included.

## Example
A 5% APR compounded monthly yields about 5.12% APY; free extra return purely from compounding twelve times a year.

Result for these inputs:

```
Effective annual yield (APY): 5.12%
```

## About this calculator
### Why banks quote both

US regulation (Truth in Savings) requires APY on deposit products precisely because nominal rates understate real earnings. When comparing accounts, compare APYs; they are directly comparable regardless of compounding style.

### Loans run the other way

For borrowing, the same math works against you: frequent compounding raises the effective cost of a nominal loan rate. Mortgage APR disclosures attempt the reverse adjustment.

## FAQs
### Which matters more, APY or compounding frequency?

APY; it already bundles frequency. A daily-compounded 4.9% nominal account can beat a monthly-compounded 4.95% one.

### What is continuous compounding?

The mathematical limit as m → ∞: APY = e^APR − 1. At 5% that is about 5.13%, barely above daily compounding.

### Is APY the same as EAR?

Yes; effective annual rate and APY describe the same concept.

## Related calculators
- [Compound Interest Calculator](https://codeasystem.com/calculators/finance/compound-interest-calculator/)
- [Simple Interest Calculator](https://codeasystem.com/calculators/finance/simple-interest-calculator/)
- [Savings Goal Calculator](https://codeasystem.com/calculators/finance/savings-goal-calculator/)

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Last updated: 2026-08-23 · Version: 1.0.0 · [HTML version](https://codeasystem.com/calculators/finance/apy-calculator/)