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APR vs APY calculator
APR and APY both describe a yearly interest rate, but they are not the same number, and the difference is money.
APR is the nominal yearly rate before compounding; APY is the effective rate once interest is added on the chosen schedule.
APR, the annual percentage rate, is the nominal rate before any compounding, a flat headline figure. APY, the annual percentage yield, is the effective rate once interest is added to the balance on a set schedule and then earns interest itself. Enter a nominal APR and how often it compounds, and this tool returns the APY it really works out to, the gap between the two in percentage points, and, if you add a balance, the interest a full year would earn or cost. Banks lean on this difference on purpose. Savings accounts advertise APY because compounding makes it look higher; loans and credit cards quote APR because it looks lower. The same 12 percent behaves differently depending on whether it lands once a year or in twelve monthly slices, and knowing which one you are being shown is the difference between comparing deals fairly and being quietly misled.
How it works
- Enter the nominal rate, the APR, as the headline annual percentage you have been quoted.
- Choose how often the interest compounds: yearly, half-yearly, quarterly, monthly or daily.
- The tool divides the APR by the number of periods to get the rate added each period.
- It compounds that period rate across a full year to find the effective annual rate, the APY.
- Add an optional balance and it shows the interest one year at that APY would produce.
APY = (1 + APR / n)^n - 1, where n is the number of compounding periods a year
Take the nominal rate, the APR, and divide it by the number of times interest is added in a year to get the rate per period. Add one, raise it to the power of the number of periods to compound it across the whole year, then subtract one to leave the effective annual rate. With n equal to one, yearly compounding, the formula collapses and APY equals APR. As n grows, the APY rises toward a ceiling set by continuous compounding, e to the power of the rate minus one.
- APR
- the nominal annual rate, before compounding
- n
- how many times interest is added per year
- APY
- the effective annual rate, after compounding
APY from a 12% APR at different compounding frequencies
| Yearly | 12.000% | no compounding within the year |
| Quarterly | 12.551% | four periods |
| Monthly | 12.683% | the worked example |
| Daily | 12.747% | close to the continuous limit |
Worked example
A savings account pays 12 percent APR, with interest added monthly: each month adds 1 percent, but because the second month earns interest on the interest from the first month, the year ends at an effective 12.68 percent APY, not 12. On a 10,000 balance that is about 1,268 over the year rather than 1,200, an extra 68 from compounding alone. Compound the same 12 percent daily instead and the APY edges up again to about 12.75 percent, close to the ceiling that continuous compounding would reach.
Key facts
- APY equals APR only when interest compounds once a year; otherwise APY is higher.
- The gap between APR and APY widens with both the rate and the compounding frequency.
- Savings products advertise APY, loans and cards advertise APR, so the figures are not directly comparable.
- Beyond daily, more frequent compounding barely moves the APY, since it nears the continuous limit.
Tips
- Always convert competing rates to APY on the same basis before deciding which account or loan wins.
- For borrowing, read the APR and check whether it includes fees, because a fee-inclusive APR is the truer cost.
- On large balances even a small APR-to-APY gap is real money, so it is worth the conversion.
- Match the compounding frequency to the product; a card that compounds daily costs more than its monthly APR hints.
Frequently asked questions
What is the difference between APR and APY?+
APR is the nominal annual rate before compounding, a flat figure. APY is the effective rate after compounding, which counts the interest that interest earns. APY is always at least as high as APR, and higher whenever interest compounds more than once a year.
Why do savings accounts quote APY but loans quote APR?+
APY is the larger number once compounding is added, so it flatters a savings rate. APR is the smaller number, so it flatters a borrowing cost. Each side shows the figure that looks better, which is why you should convert to a common basis before comparing.
Does more frequent compounding always help?+
For money you are owed, yes: daily compounding beats monthly beats yearly at the same nominal rate. For money you owe it works against you, since the debt grows faster. The effect shrinks as frequency rises, so the jump from yearly to monthly matters more than monthly to daily.
Is APR the same as the interest rate on my loan?+
Not always. A true APR can also fold in compulsory fees, which lifts it above the plain interest rate. This calculator works on the rate alone, so a fee-loaded APR will cost more than the comparison here suggests.
How do I compare two savings accounts fairly?+
Convert both to APY using the compounding frequency of each account, then compare the APYs. An account at 4.9 percent compounded daily can beat one at 5 percent paid once a year, so the headline rate alone can mislead.
What is the most an APY can reach for a given rate?+
As compounding gets infinitely frequent, the APY approaches the mathematical constant e raised to the nominal rate, minus one. At 12 percent that limit is about 12.75 percent, which is why daily compounding already sits very close to the theoretical maximum.
Things to watch
- A headline rate with no stated compounding frequency cannot be compared honestly, so ask how often it compounds.
- This tool works on the rate alone and ignores fees, so a fee-loaded loan APR will cost more than shown.
- Tax on savings interest is not deducted here, so the amount you keep on a deposit can be lower than the figure given.
Last updated: 2026
This is an estimate for general guidance, not financial, tax, legal or medical advice. Figures can change and individual circumstances vary. Always confirm with an official source before making decisions.
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