Calculator 01 · Rates
The APR is the rate on the label. The APY is what a year of compounding does with it. Enter either one, pick how often interest is added, and see both side by side at every frequency.
Your figuresp. 1
The answerp. 2
APY · Monthly5.116%
A year's interest on $10,000.00$511.62
An APR of 5.00% compounded monthly grows by 5.116% over a year. The APY is 0.116% points higher because interest earns interest.
| Line | Compounding | Times a year | Rate per period | APY | A year's interest |
|---|---|---|---|---|---|
| 01 | Annually | 1 | 5.0000% | 5.000% | $500.00 |
| 02 | Semi-annually | 2 | 2.5000% | 5.063% | $506.25 |
| 03 | Quarterly | 4 | 1.2500% | 5.095% | $509.45 |
| 04 | Monthly (chosen) | 12 | 0.4167% | 5.116% | $511.62 |
| 05 | Twice a month | 24 | 0.2083% | 5.122% | $512.16 |
| 06 | Every two weeks | 26 | 0.1923% | 5.122% | $512.21 |
| 07 | Weekly | 52 | 0.0962% | 5.125% | $512.46 |
| 08 | Daily (365) | 365 | 0.0137% | 5.127% | $512.67 |
| 09 | Continuously | ∞ | — | 5.127% | $512.71 |
Educational use only — not financial advice. The rate is whatever you type in; nothing here is an offer, a quote or a forecast.
An APR (annual percentage rate) is a yearly rate before compounding. Divide it by the number of compounding periods and you get the rate added each period: 5% APR compounded monthly is 0.4167% a month. The APY (annual percentage yield) is what that does over a whole year once each period's interest starts earning interest of its own.
APY = (1 + APR ÷ n)n − 1
continuous: APY = eAPR − 1
back again: APR = n × ((1 + APY)1/n − 1)
Worked example: 0.05 ÷ 12 = 0.0041667, and 1.004166712 = 1.05116, so 5% APR compounded monthly is an APY of 5.116%. On $10,000 that is $511.62 in a year rather than $500.
US savings accounts quote an APY because the Truth in Savings rules (Regulation DD) require it, worked out as APY = 100 × [(1 + interest ÷ principal)365 ÷ days in term − 1]. Loans and credit cards quote an APR under the Truth in Lending rules (Regulation Z). The same arithmetic runs in reverse on debt: a 22% card APR charged daily grows an unpaid balance by about 24.6% a year.
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Try WebTraceCheckThe APY. It already includes compounding, so accounts that add interest on different schedules can be compared directly. Comparing two APRs only works when both compound on the same schedule.
Less than you might expect at savings rates: 5% APR is 5.116% compounded monthly and 5.127% daily. The gap grows with the rate. At 22% the step from monthly (24.36%) to daily (24.60%) is about a quarter of a point.
Interest added in infinitely small steps. It is the mathematical ceiling for a given APR: APY = e^APR − 1, so 5% continuous gives 5.127%, a hair above daily. You meet it more in finance textbooks than on account statements.
No. With compounding once a year the two are equal, and more frequent compounding can only push the APY above the APR. If you see a lower APY than APR, check that both figures describe the same account and the same compounding.