APR to APY Converter
Convert a nominal annual rate (APR) to the effective annual rate (APY) it produces, or work backwards from an APY to the APR. Pick the compounding frequency — annual up to daily, or continuous — and see the formula worked out with your numbers and the same rate at every frequency. Free, no sign-up.
Your rate
Results
6.167781%
Effective annual rate (APY)
6%
Nominal annual rate (APR)
0.5%
Rate per compounding period
0.167781%
Difference between APY and APR
$616.78
Interest after one year
The working
APY = (1 + APR ÷ m)^m − 1 = (1 + 0.06 ÷ 12)^12 − 1 = 6.167781%
The same APR at every compounding frequency
| Compounding | Times per year | APR | APY |
|---|---|---|---|
| Annually (1 per year) | 1 | 6% | 6% |
| Semiannually (2 per year) | 2 | 6% | 6.09% |
| Quarterly (4 per year) | 4 | 6% | 6.1364% |
| Every two months (6 per year) | 6 | 6% | 6.152% |
| Monthly (12 per year) | 12 | 6% | 6.1678% |
| Twice a month (24 per year) | 24 | 6% | 6.1757% |
| Every two weeks (26 per year) | 26 | 6% | 6.1763% |
| Weekly (52 per year) | 52 | 6% | 6.18% |
| Daily (365 per year) | 365 | 6% | 6.1831% |
| Continuously | ∞ | 6% | 6.1837% |
This converts between a nominal and an effective annual rate and includes no fees. A loan's regulatory APR can include fees, so it is not always the plain nominal rate.
How to Use the APR to APY Converter
- 1. Choose the direction. APR to APY starts from a nominal rate and finds the effective rate; APY to APR starts from the effective rate and finds the nominal rate that would produce it.
- 2. Enter the rate. As a percentage: 6 for 6%.
- 3. Choose the compounding. How many times a year interest is added to the balance, or continuously. A savings account often compounds daily or monthly; a credit card usually compounds daily.
- 4. Read the result. The converted rate, the rate per compounding period and the gap between APY and APR appear with the working. Add a balance to see the interest it would earn in one year at the APY.
- 5. Compare frequencies. The table shows the same rate at every compounding frequency, so you can see how much the schedule matters.
APR, APY and the Formulas
The APR used here is the nominal annual rate: the periodic rate multiplied by the number of periods in a year. The APY is the effective annual rate: the rate that, applied once a year, grows the balance by the same amount as the nominal rate does after compounding. With m compounding periods a year:
- APY = (1 + APR ÷ m)m − 1
- APR = m × [(1 + APY)1/m − 1]
- Continuous compounding: APY = eAPR − 1, and APR = ln(1 + APY).
Because each period's interest earns interest in the next, the APY is always at least the APR, and equal to it only when interest compounds once a year. The more often interest compounds, the higher the APY for the same APR — but the increase shrinks quickly, and continuous compounding is the ceiling.
| Compounding | APY |
|---|---|
| Annually | 6.0000% |
| Semiannually | 6.0900% |
| Quarterly | 6.1364% |
| Monthly | 6.1678% |
| Daily (365) | 6.1831% |
| Continuously | 6.1837% |
Worked Examples
- Savings. A 6% APR compounded monthly is 0.5% a month: (1.005)12 − 1 = 6.1678% APY. On a balance of 10,000, one year of interest is 616.78, not the 600.00 a simple reading of 6% would suggest.
- Debt. A credit-card APR of 24% compounded daily has an APY of (1 + 0.24 ÷ 365)365 − 1 = 27.1149%. Compounded monthly, the same APR is 26.8242%.
- Backwards. To earn an effective 5% a year with monthly compounding you need a nominal rate of 12 × (1.051/12 − 1) = 4.8889%. Compounded continuously, it is ln(1.05) = 4.8790%.
What 'APR' and 'APY' mean on a real product
In the United States, deposit accounts quote an APY under Regulation DD, whose formula is APY = 100 × [(1 + Interest ÷ Principal)365 ÷ days in term − 1]. Loan and card APRs follow other rules, and a loan's disclosed APR can include fees, so it is not always the plain nominal rate used in this converter. For a real product, use the figures in its disclosure. Other countries define these terms differently. See the Regulation DD appendix for the deposit-account definition.
Why the Difference Matters
APY is the right figure for comparing deposits that compound at different frequencies, because it puts them on the same once-a-year footing. For borrowing, the gap works against you: a card that compounds daily costs more than its APR suggests. The calculator does not say which rate you should accept — it converts one into the other.
Frequently Asked Questions
- How do I convert APR to APY?
- Divide the APR by the number of compounding periods per year, add 1, raise the result to the power of the number of periods, then subtract 1: APY = (1 + APR ÷ m)m − 1. For 6% compounded monthly that gives 6.1678%.
- Is APY always higher than APR?
- Whenever interest compounds more than once a year, yes. If it compounds once a year, APY and APR are equal. The more frequent the compounding, the larger the gap, up to the limit of continuous compounding.
- How do I convert APY to APR?
- Use APR = m × [(1 + APY)1/m − 1]. An APY of 5% with monthly compounding corresponds to a nominal APR of 4.8889%. Switch the converter to APY to APR to do this with the working shown.
- What is the formula for continuous compounding?
- APY = eAPR − 1, where e is about 2.71828. It is the limit of the discrete formula as the number of periods grows without bound. A 6% APR compounded continuously is an APY of 6.1837%.
- Why does a credit card's effective rate exceed its APR?
- Card interest is typically charged on a daily balance and added to it, so interest compounds. A 24% APR compounded daily is an effective 27.1149% a year. A card's disclosed APR is set under consumer-credit rules, so check its own terms.
- Which is better for comparing savings accounts, APR or APY?
- APY, because it already includes the effect of compounding, so accounts with different compounding schedules compare directly. Two accounts quoting the same APR can pay different APYs.