Understanding the Effective Annual Rate
The Effective Annual Rate (EAR) is the true annual interest rate after accounting for the effect of compounding. While a nominal rate (APR) tells you the stated annual percentage, the EAR reveals what you actually earn on savings or pay on loans when interest compounds multiple times per year. In 2026, with varying compounding frequencies across savings accounts, CDs, and loan products, using EAR is the only reliable way to compare financial products on an equal basis.
The EAR Formula
The Effective Annual Rate is calculated using the nominal annual interest rate and the number of compounding periods per year:
EAR = (1 + r / n)^n - 1
Where:
r= nominal annual interest rate (as a decimal)n= number of compounding periods per year
For continuous compounding, the formula becomes:
EAR = e^r - 1
The calculator also computes:
- Periodic Rate = r / n (the rate applied each compounding period)
- Compounding Gain = EAR - r (the extra return from compounding)
- Interest on $10,000 = 10,000 x EAR (dollar interest earned in one year)
Worked Example: 6% Nominal Rate Compounded Monthly
Given a nominal annual interest rate of 6% compounded monthly (12 times per year):
- Convert to decimal: r = 6% = 0.06
- Calculate periodic rate: 0.06 / 12 = 0.005 (0.5000% per period)
- Apply the EAR formula: EAR = (1 + 0.005)^12 - 1 = 1.06167781 - 1 = 0.06167781
- Convert to percentage: EAR = 6.1678%
- Compounding gain: 6.1678% - 6.0000% = 0.1678%
- Interest on $10,000: $10,000 x 0.06167781 = $616.78
The 6% nominal rate compounded monthly produces an effective annual rate of 6.1678%. On a $10,000 deposit, you earn $616.78 in interest — $16.78 more than the $600.00 you would earn with simple annual compounding.
How Compounding Frequency Changes EAR
For a 6% nominal rate, here is how different compounding frequencies compare:
| Compounding | Periods (n) | EAR |
|---|---|---|
| Annually | 1 | 6.0000% |
| Semi-annually | 2 | 6.0900% |
| Quarterly | 4 | 6.1364% |
| Monthly | 12 | 6.1678% |
| Weekly | 52 | 6.1800% |
| Daily | 365 | 6.1831% |
| Continuously | Infinite | 6.1837% |
The largest jump occurs between annual and quarterly compounding (+0.1364 points). After monthly compounding, the marginal gains are minimal — going from monthly to daily adds only 0.0153 percentage points.
EAR for Investors and Borrowers
For investors, EAR is the key metric when comparing savings accounts, CDs, and money market funds. A bank advertising 5.9% compounded daily (EAR: 6.08%) actually delivers a higher return than one offering 6.0% compounded annually (EAR: 6.00%). The Federal Deposit Insurance Corporation (FDIC) requires banks to disclose the Annual Percentage Yield (APY), which is identical to EAR, for exactly this reason.
For borrowers, EAR reveals the true cost of debt. A credit card with an 18% APR compounded monthly has an EAR of 19.56%, meaning the actual annual interest burden is 1.56 percentage points higher than the advertised rate. Understanding this difference helps borrowers evaluate loan offers accurately.
Practical Applications of EAR
Certificate of Deposit (CD) comparison: When choosing between CDs from different banks, convert each quoted APR to EAR using this calculator. The CD with the highest EAR gives the best return, regardless of how the rate is quoted.
Mortgage shopping: Two mortgage lenders might both advertise 7% APR but with different compounding. Monthly compounding (standard in the U.S.) gives an EAR of 7.23%, while semi-annual compounding (common in Canada) gives 7.12%. This difference matters over a 30-year term.
Credit card cost awareness: Most credit cards compound daily on unpaid balances. A 22% APR compounded daily has an EAR of 24.60%, adding 2.60 percentage points to the true annual cost compared to what the card issuer advertises.