Enter the annual nominal rate and the number of compounding periods per year into the calculator to determine the effective interest rate.
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Effective Interest Rate Formula
The following formula is used to calculate an effective interest rate.
ER = (1 + i/n) ^ n - 1
- Where ER is the effective interest rate
- i is the nominal annual interest rate (as a decimal)
- n is the number of compounding periods per year
Effective Interest Rate Definition
The Effective Interest Rate (also called the effective annual rate, EAR) is a financial metric that measures the actual annual cost of borrowing or annual return on an investment after accounting for compounding.
Rather than solely considering the nominal interest rate, the effective interest rate reflects the interest earned or paid when interest is compounded within the year. (Any fees or charges are not included unless they are incorporated into the rate/cash flows being analyzed.)
Effective Interest Rate Example
How to calculate an effective interest rate.
- First, determine the nominal rate.
For this example, we will say we are looking at a credit card with an annual nominal rate (APR) of 0.15 (15%), compounded monthly.
- Next, determine the compounding periods per year.
Since the interest is compounded monthly, the number of compounding periods per year is 12.
- Finally, calculate the effective interest rate.
Using the formula above we find the effective rate to be (1 + 0.15/12)^12 – 1 = 0.1607 (16.07%).
FAQ
How does compounding affect the effective interest rate?
For a given nominal rate, compounding increases the effective interest rate because interest is earned on previously accumulated interest in addition to the principal amount. In general, the more frequently interest is compounded (e.g., monthly vs. annually), the higher the effective annual rate will be.
Why is the effective interest rate important?
The effective interest rate provides a more accurate measure of the cost of borrowing or the return on investment than the nominal rate alone because it accounts for compounding.
Can the effective interest rate be lower than the nominal rate?
No, the effective interest rate is always equal to or higher than the nominal rate (when the nominal rate is quoted as an annual rate compounded within the year). The common case where they are equal is when interest is compounded once per year (or effectively not compounded within the year).
How can I lower the effective interest rate on a loan?
To lower the effective interest rate, you can choose a loan with fewer compounding periods, make more frequent payments to reduce the principal faster, or negotiate a lower nominal interest rate with the lender.
