Effective Annual Rate Calculator
This effective annual rate calculator converts a nominal annual rate, the kind quoted as an APR or an interest rate “compounded monthly,” into the rate you actually earn or pay over a year once interest compounds. It also works the other way, turning an effective rate such as an APY back into the nominal rate and the periodic rate behind it, and compares every compounding frequency in one table.
Updated
Results
- Periodic rateNominal rate ÷ periods: the rate applied each period
- Simple split of your rateRate entered ÷ periods
- Equivalent periodic rateCompounds back to the rate entered
- Compounding periods per year
- Effective minus nominalIn percentage points
| Compounding | Periods per year | Nominal rate | Effective rate | Periodic rate |
|---|
Results are estimates. See the methodology below.
How to use the calculator
- Direction: choose nominal → effective if you have a quoted annual rate, or effective → nominal if you have an APY or effective rate and want the rate behind it.
- Rate: the annual rate in percent, for example 5 or 24.
- Compounding: how often interest is added: daily (365 times a year), monthly, quarterly, semiannually, annually or continuously.
The result shows the converted rate, the rate applied each period and the gap between effective and nominal. The table repeats the conversion for every frequency. Period figures are not shown for continuous compounding, which has no discrete periods.
The formulas
With a nominal rate r compounded n times a year:
EAR = (1 + r/n)^n − 1
For continuous compounding, EAR = e^r − 1. In reverse, r = n × ((1 + EAR)^(1/n) − 1), or ln(1 + EAR) for continuous compounding.
The periodic rate is the nominal rate divided by n: what is actually charged or credited each period. The calculator also shows two ways to split the rate you entered into periods:
- Simple split = rate ÷ n. This treats your number as a nominal rate. US lenders build APRs this way: Regulation Z says the APR for open-end credit is computed by multiplying the periodic rate by the number of periods in a year.
- Equivalent periodic rate = (1 + rate)^(1/n) − 1. This treats your number as an effective rate: compounding it n times gives back exactly the annual rate.
At 12%, the simple split is 1% a month, while the equivalent monthly rate is 0.9489%. Daily compounding uses 365 days; leap years and other day-count conventions are not modeled.
Examples
1. 5% at every compounding frequency
| Compounding | Periodic rate | Effective annual rate |
|---|---|---|
| Annually | 5.0000% | 5.0000% |
| Semiannually | 2.5000% | 5.0625% |
| Quarterly | 1.2500% | 5.0945% |
| Monthly | 0.4167% | 5.1162% |
| Daily | 0.0137% | 5.1267% |
| Continuously | — | 5.1271% |
More frequent compounding raises the effective rate, but the gain shrinks quickly: daily is only 0.0004 points behind continuous.
2. A 24% credit card APR
Split monthly, 24% is a 2% periodic rate and an effective annual rate of 26.8242%. With a daily periodic rate of 0.0658%, the effective rate is 27.1149%. That only applies if the balance and interest stay unpaid all year.
3. From APY back to the nominal rate
A savings account advertising a 4.50% APY with daily compounding has a nominal rate of 4.4020% and a daily rate of 0.0121%. If a 6% effective rate is compounded monthly, the nominal rate is 5.8411% and the monthly rate 0.4868%, not 0.5%.
APR, APY and EAR
An APR is a nominal annual rate: the periodic rate multiplied by the number of periods. On a mortgage or other loan, the CFPB notes it also reflects points, broker fees and other charges, so it is usually higher than the interest rate. An APY on a deposit includes compounding; Regulation DD bases it on the interest a deposit earns over a 365-day year, the same idea as an effective annual rate. To compare offers, convert both to effective rates. For a loan's full APR with fees, use our APR calculator; for savings growth, our APY calculator.
Frequently asked questions
What is the effective annual rate?
It is the rate you really earn or pay in one year once interest on interest is included. A 5% rate compounded monthly gives an EAR of 5.1162%.
Is APY the same as the effective annual rate?
Both measure the yearly return including compounding, and for an account that compounds at a fixed rate they give the same figure. APY is the term US banks must use for deposit accounts under Truth in Savings; EAR is the general finance term.
Why is my credit card's real rate higher than the APR?
Because the APR is the periodic rate times the number of periods and does not include compounding. If you carry a balance and interest is added to it, you pay interest on that interest, so the effective rate is higher. At 24% the difference is about 2.8 to 3.1 points.
Does daily compounding make a big difference compared with monthly?
Usually not. At 5% the effective rate is 5.1267% with daily compounding and 5.1162% with monthly, a gap of about one hundredth of a point. The gap grows with the rate: at 24%, daily compounding adds 0.29 points over monthly.
What is continuous compounding?
It is the limit as the number of periods becomes infinite. The effective rate is e^r − 1, so 5% compounded continuously equals 5.1271%. It is mostly used in financial theory and option pricing rather than consumer accounts.
Sources
Results are mathematical conversions for comparison purposes. The rates and fees in your loan or account disclosures are the ones that apply.