APR / APY converterAPR to APY calculator: convert compounding rates
Convert a nominal annual interest rate to an effective annual yield, or reverse the calculation, for a fixed compounding frequency. At 12% nominal compounded monthly, the effective yield is about 12.68%. The APR label here means a nominal rate for this mathematical conversion. A legally disclosed borrowing APR can include fees and other finance charges. This tool does not compute regulatory loan APR, predict a credit-card bill, or compare the full cost of borrowing with deposit returns.
Converted APY
$13
12.00% nominal rate · monthly compounding
Same nominal rate, every compounding frequency
The APY of 12.00% APR across the four standard frequencies — more compounding periods always mean a higher effective rate.
How to use
- 1
Choose nominal rate to APY, or APY to nominal rate.
- 2
Enter the percentage and select annual, quarterly, monthly, or daily compounding.
- 3
Read the converted rate and compare the effective yields across frequencies.
- 4
Check the assumptions: no fees, transactions, or rate changes are modeled.
Benefits
Compounding explained
See how a nominal rate differs from its effective annual yield.
Four frequencies
Compare annual, quarterly, monthly, and daily compounding.
Reverse conversion
Recover a nominal rate from an effective yield and frequency.
APR vs. APY — where each term appears
Lenders use APR; savings accounts use APY. Knowing which is which prevents you from comparing apples to oranges when evaluating rates.
| Product | Rate shown | Compounding | Why it matters |
|---|---|---|---|
| Credit card | APR | Daily (365×) | True cost is higher than the stated APR |
| Mortgage | APR | Monthly (12×) | APR here also includes fees — not purely rate |
| Auto loan | APR | Monthly (12×) | Compare APRs across lenders directly |
| High-yield savings (HYSA) | APY | Daily or monthly | Higher compounding = higher effective yield |
| CD (certificate of deposit) | APY | Daily or monthly | APY already reflects compounding — use directly |
| Money market account | APY | Daily | Compare APY to APY — no conversion needed |
How compounding frequency changes your effective rate
At the same 12% nominal APR, here is how much the APY changes by compounding frequency:
| Compounding | Periods/yr | APY (12% nominal) |
|---|---|---|
| Annual | 1 | 12.00% |
| Quarterly | 4 | 12.55% |
| Monthly | 12 | 12.68% |
| Daily | 365 | 12.75% |
The difference seems small, but on a $50,000 balance over 10 years, annual vs. daily compounding at 12% nominal produces a difference of over $6,000 in ending value.
How it works
- APR
- Nominal annual interest rate in this model; excludes loan fees
- APY
- Annual Percentage Yield — the effective yearly rate after compounding
- n
- Compounding periods per year (1 = annual, 4 = quarterly, 12 = monthly, 365 = daily)
For nominal annual rate r and n equal compounding periods, effective yield = (1 + r/n)^n - 1. The inverse is r = n * ((1 + yield)^(1/n) - 1). Use decimals in these equations; the form displays percentages. Assumptions: constant rates, reinvested interest, no fees, and no cash flows. Daily mode uses 365 periods.
Worked example
A hypothetical balance earns 12% nominal annual interest with monthly compounding. Applying APY = (1 + 0.12 ÷ 12)^12 − 1 gives 12.68% effective annual yield before fees. The same nominal 12% is worth 12.55% APY compounded quarterly and 12.75% APY compounded daily, which is why the frequency always matters.
Understanding your results
The effective annual yield reflects compounding at the selected frequency under a constant-rate, no-fee model. The nominal rate shown is for mathematical conversion; it is not a fee-inclusive regulatory loan APR or an estimate of a credit-card bill.
Sources and methodology
These resources explain related concepts. They do not certify or endorse this calculator. See the assumptions and worked example above.
- Interest rate and APR — CFPB ↗
Explains why a borrowing APR can include charges beyond the interest rate.
- Truth in Savings: Annual Percentage Yield — FDIC ↗
Describes APY as reflecting the interest rate and compounding frequency over a year; account disclosures and terms still apply.
Frequently asked questions
It is shorthand for the nominal annual interest rate used in the compounding formula. Disclosed loan APR can include fees and must not automatically be substituted for that rate.
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Open calculatorFigures are estimates for education only — not financial advice. Results depend on the assumptions you enter. Read the full disclaimer.