# APY Calculator

> Converts a nominal annual rate (APR) into the effective annual yield (APY) for a given compounding frequency, and reports the periodic rate and the one-year growth of 1,000.

- Calculator id: `apy` · Category: Finance (`finance`) · Tool name: `convert_apr_to_apy`
- Canonical page: https://tttkmbb.com/finance/apy · This document: https://tttkmbb.com/finance/apy.md · JSON definition: https://tttkmbb.com/finance/apy.json

## Purpose

Converts a nominal annual rate (APR) into the effective annual yield (APY) for a given compounding frequency, and reports the periodic rate and the one-year growth of 1,000.

**Use when:** You want to compare deposit accounts or loans quoted with different compounding frequencies, or need the effective annual rate for a nominal rate.

**Do not use when:** You need a balance after several years or with deposits (use compound-interest), or the account quotes an APY already and you want the nominal rate (enter it as annual compounding).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `apr_percent` | number | % | required | Stated annual rate in percent before compounding; 5 means 5 %. (min 0, max 1000) |
| `compounding_frequency` | enum: annually \| semiannually \| quarterly \| monthly \| weekly \| daily |  | optional, default "monthly" | How often interest is credited: n = 1, 2, 4, 12, 52 or 365 periods per year. |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `apy_percent` | number | % | (1 + APR/n)^n − 1, in percent. |
| `periodic_rate_percent` | number | % | APR / n, the rate applied each compounding period. |
| `periods_per_year` | integer |  | n for the chosen compounding frequency. |
| `apy_minus_apr_percentage_points` | number | percentage points | Extra yield produced by compounding within the year. |
| `balance_of_1000_after_one_year` | number |  | 1000 × (1 + APY). |

## Formula

`APY = (1 + apr_percent/100 / n)^n − 1, where n = compounding periods per year (1, 2, 4, 12, 52 or 365)`

This is the effective-annual-rate formula prescribed by US Regulation DD (Truth in Savings) for deposit accounts; it ignores fees and assumes the rate stays constant for a year.

## Data Sources

- Investopedia – Annual Percentage Yield (APY): What It Is and How It Works — https://www.investopedia.com/terms/a/apy.asp (reference, retrieved 2026-09-23)
- 12 CFR Part 1030 – Truth in Savings (Regulation DD), Appendix A: APY calculation — https://www.ecfr.gov/current/title-12/chapter-X/part-1030 (government, retrieved 2026-09-23)
- Wikipedia – Effective interest rate — https://en.wikipedia.org/wiki/Effective_interest_rate (reference, retrieved 2026-09-23)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/apy?apr_percent=…`
- `POST https://tttkmbb.com/api/v1/calculate/apy` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/apy · OpenAPI operationId `convert_apr_to_apy` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "apy", "inputs": {…}}`

## Example

- 5 % APR compounded monthly: inputs `{"apr_percent":5,"compounding_frequency":"monthly"}` → `{"apy_percent":5.1162,"periodic_rate_percent":0.416667,"periods_per_year":12,"apy_minus_apr_percentage_points":0.1162,"balance_of_1000_after_one_year":1051.16}`
- 4 % APR compounded daily: inputs `{"apr_percent":4,"compounding_frequency":"daily"}` → `{"apy_percent":4.0808,"periods_per_year":365,"balance_of_1000_after_one_year":1040.81}`

```
GET https://tttkmbb.com/api/v1/calculate/apy?apr_percent=5&compounding_frequency=monthly
```

## Limitations

You need a balance after several years or with deposits (use compound-interest), or the account quotes an APY already and you want the nominal rate (enter it as annual compounding). This is the effective-annual-rate formula prescribed by US Regulation DD (Truth in Savings) for deposit accounts; it ignores fees and assumes the rate stays constant for a year. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

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

APR is the nominal rate before compounding; APY is the rate you actually earn (or pay) in a year once interest is compounded. They are equal only with annual compounding.

**How do I go from APY back to APR?**

APR = n × ((1 + APY)^(1/n) − 1). For 5.1162 % APY with monthly compounding that gives 5.00 % APR.

## Related

- [Compound Interest Calculator](https://tttkmbb.com/finance/compound-interest.md) — Grow a balance at this rate over several years.
- [Rule of 72 Calculator](https://tttkmbb.com/finance/rule-of-72.md) — Estimate how long the rate takes to double money.