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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.

When to use

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).

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.

Inputs

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

Outputs

Output	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).

Example

5 % APR compounded monthly: {"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: {"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

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/apy (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/apy · Markdown: https://tttkmbb.com/finance/apy.md · JSON definition: https://tttkmbb.com/finance/apy.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="apy"
OpenAPI operationId: convert_apr_to_apy
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Investopedia – Annual Percentage Yield (APY): What It Is and How It Works (reference)
12 CFR Part 1030 – Truth in Savings (Regulation DD), Appendix A: APY calculation (government)
Wikipedia – Effective interest rate (reference)

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 calculators

Compound Interest Calculator — Grow a balance at this rate over several years.
Rule of 72 Calculator — Estimate how long the rate takes to double money.