How to use the Effective Annual Rate (EAR) Calculator
- Enter the nominal (stated) annual interest rate.
- Choose how often it compounds, from yearly to daily or continuously.
- Optionally enter a sample amount to see the interest over one year.
- Read the effective annual rate and the extra it adds over the nominal rate.
Formula used
EAR = (1 + r ÷ m)^m − 1, where r is the nominal annual rate and m the number of compounding periods per year. For continuous compounding, EAR = e^r − 1.
Worked example
Here is the Effective Annual Rate (EAR) Calculator worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| Nominal annual rate | 12 % |
| Compounding | Monthly |
| Sample amount | $100,000 |
| Result | |
| Effective annual rate | 12.68% |
| Extra over the nominal rate | 0.68% |
| Interest on the sample amount in one year | $12,682.50 |
| Balance after one year | $112,682.50 |
Effective rate by compounding frequency
For a nominal rate of 12%.
| Compounding | Effective annual rate |
|---|---|
| 1 | 12% |
| 2 | 12.36% |
| 4 | 12.55% |
| 12 | 12.68% |
| 365 | 12.75% |
The formula
EAR = (1 + r ÷ m)^m − 1, where r is the nominal annual rate and m the number of compounding periods a year. For 12% compounded monthly, EAR = (1 + 0.12 ÷ 12)^12 − 1 = 12.6825%. That is 0.6825 percentage points above the stated rate.
On $100,000, one year of interest at that effective rate is $12,682.50, leaving $112,682.50. With yearly compounding the same 12% would give exactly $12,000.00.
More frequent compounding
The more often interest compounds, the higher the effective rate, but with diminishing returns. At 12% nominal, yearly compounding gives 12%, monthly 12.6825%, daily 12.7475% and continuous compounding 12.7497%, which is the limit, e^0.12 − 1.
At lower rates the gap is smaller. An 8% nominal rate compounded quarterly has an EAR of 8.2432%.
EAR, APY and APR
For savings, the effective annual rate is usually called the annual percentage yield (APY). Banks in many countries must show it so that accounts with different compounding can be compared. For borrowing, the annual percentage rate (APR) is a different measure that normally includes some fees and is not always the same as the effective rate.
When comparing, always compare like with like: EAR to EAR, or APY to APY. A loan advertised at a lower nominal rate but compounding more often can cost as much as one with a higher nominal rate that compounds yearly.
Using it to compare offers
Suppose one deposit pays 7.2% compounded monthly and another 7.3% compounded yearly. Converting the first gives about 7.44% and the second stays at 7.3%, so the lower stated rate is the better deal.
To project a balance over several years, use the compound interest calculator. To find the rate that doubles your money, see the rule of 72 calculator.
Frequently asked questions
What is the effective annual rate?
The yearly growth rate after allowing for compounding within the year.
Is EAR the same as APY?
Yes, for savings and deposits. APY is the effective annual rate.
Why is EAR higher than the nominal rate?
Interest is added several times a year, so later interest is earned on interest already added.
What is continuous compounding?
The limit as compounding becomes infinitely frequent. The formula is e^r − 1.
Does EAR include fees?
No. It reflects compounding only. Fees and charges change what you actually pay or receive.
Is EAR the same as APR?
No. APR is a loan measure that often includes some fees and usually does not capture compounding the same way.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.