The effective interest rate (also called the effective annual rate, EAR) is the actual annual interest rate accounting for compounding within the year. It provides a true measure of the cost of borrowing or the return on an investment.
How to Find the Effective Interest Rate
- Identify the nominal interest rate (i) — the stated annual interest rate.
- Determine the number of compounding periods per year (n) — how often interest is compounded (e.g., annually, semi-annually, quarterly, monthly).
- Apply the formula:
Effective Interest Rate (EIR)=(1+in)n−1\text{Effective Interest Rate (EIR)}=\left(1+\frac{i}{n}\right)^n-1Effective Interest Rate (EIR)=(1+ni)n−1
Where:
- iii is the nominal annual interest rate expressed as a decimal (e.g., 6% = 0.06)
- nnn is the number of compounding periods per year
- Convert the result into a percentage by multiplying by 100 if needed.
Explanation and Impact of Compounding
- More frequent compounding periods increase the effective interest rate. For example, monthly compounding produces a higher effective rate than annual compounding with the same nominal rate.
- This formula allows for comparison between loans or investments with different compounding frequencies on an "apples-to-apples" basis.
Example
For a nominal rate of 6% compounded monthly (12 times a year):
EIR=(1+0.0612)12−1=0.06168 or 6.168%EIR=\left(1+\frac{0.06}{12}\right)^{12}-1=0.06168\text{ or }6.168%EIR=(1+120.06)12−1=0.06168 or 6.168%
This is higher than the nominal 6% rate due to monthly compounding. This formula and approach provide a precise way to find the effective interest rate, ensuring accurate comparison and financial decision-making.
