The Effective Annual Rate (EAR) Calculator helps you understand the true annual interest rate you earn or pay when compounding is involved. This tool is especially helpful when comparing loans, credit cards, or investment opportunities that have different compounding frequencies.
The EAR Calculator belongs to the Financial Interest and Investment Calculators category.
Many financial products advertise a nominal interest rate, which doesn't account for how often interest is added to your balance. But with compounding, the real cost or return can be significantly different. That’s where the EAR comes in—it shows the actual annual return or cost by including the impact of multiple compounding periods.
formula of Effective Annual Rate Calculator (EAR)
Formula:
EAR = (1 + (Nominal Rate / Number of Compounding Periods per Year))^Number of Compounding Periods per Year - 1
Detailed Explanation of Variables and Calculations
EAR (Effective Annual Rate):
This is the true annual interest rate, considering how often the interest is compounded. It gives a more accurate picture of the cost of borrowing or the return on investment.
Nominal Rate:
The stated interest rate (e.g., 5% = 0.05). It does not include the effect of compounding.
Number of Compounding Periods per Year:
This tells us how frequently the interest is applied to the balance in one year:
- 1 = Annually
- 2 = Semi-annually
- 4 = Quarterly
- 12 = Monthly
- 365 = Daily (some banks use 360)
^ (Exponentiation):
This symbol means we raise the entire expression to the power of the number of compounding periods per year.
Key Insight:
The more frequently interest is compounded, the higher the EAR will be, even if the nominal rate stays the same.
Table for Common Nominal Rates and Compounding Periods
This table shows approximate EAR values for commonly used interest rates and compounding frequencies:
| Nominal Rate | Annually | Semi-Annually | Quarterly | Monthly | Daily (365) |
|---|---|---|---|---|---|
| 5% | 5.00% | 5.06% | 5.09% | 5.12% | 5.13% |
| 10% | 10.00% | 10.25% | 10.38% | 10.47% | 10.52% |
| 12% | 12.00% | 12.36% | 12.55% | 12.68% | 12.75% |
| 15% | 15.00% | 15.56% | 15.87% | 16.08% | 16.18% |
Use this chart to quickly compare the real return or cost depending on how often the rate is compound.
Example of Effective Annual Rate Calculator (EAR)
Let’s say you’re offer a loan with a nominal rate of 10%, compounded monthly.
Step 1: Identify the Variables
Nominal Rate = 0.10
Number of Compounding Periods per Year = 12
Step 2: Apply the Formula
EAR = (1 + (0.10 / 12))^12 - 1
EAR ≈ 1.1047 - 1 ≈ 0.1047 or 10.47%
Conclusion:
Although the nominal rate is 10%, the real annual rate you're paying is 10.47% due to monthly compounding.
Most Common FAQs
A: Because it includes the effect of compounding. The more frequently interest is add to your balance, the more interest it earns or accumulates.
A: Use EAR when you want to compare financial products with different compounding periods. APR may not include the full compounding effect.
A: Yes. EAR is commonly use to evaluate investments, especially when returns are compound more than once per year.