Effective Interest Rate Calculator
In the following, you can learn what is the effective interest rate, how to calculate effective interest rate on a loan with the effective interest rate formula, and what is the difference between nominal vs. effective interest rate.
What is effective interest rate?
The effective interest rate (EIR) is an annual rate that reflects the effect of compounding in a year, and result in the same future value of the money as compounding at the periodic rate for
m times a year.
For example, if you have a credit card that has a 36 percent annual interest rate, but interest is calculated and added to your balance daily, your daily interest rate is 0.1 percent (
36% / 360 = 0.1%) and compounding happens each day on a new balance (
m = 360). When interest addition and recalculation occurs more often than once a year, the annual growth on your balance will be larger than what the annual interest rate suggests, resulting in a higher finance charge (in our example 43.307%).
When you have a nest egg or investment, however, the effect of compounding becomes your friend. In this case, the more frequently interest is added to your money, the more interest that is earned on interest, meaning you get even more money. Therefore, the higher the compounding frequency, the higher the future value (FV) of your investment. If you are wondering how different compounding frequencies affect future values, check the table in our EAR calculator where you can see more details on this subject.
The effective interest rate formula - How to calculate the effective interest rate on loan?
The EIR formula in finance takes the following general form:
EIR = (1 + r / m)ᵐ − 1
EIR- The effective interest rate;
r- The annual interest rate, which is the nominal interest rate in percent, also called the stated or quoted rate; and
m- Compounding periods, which is the number of times compounding occurs in a year. In other words, the period after which the interest will be calculated on the principal amount and then added to it (capitalized on it).
If the compound frequency is continuous, you need to apply another equation:
EIR = eᵐ − 1
e stands for constant of exponent.
Note, that continuous compounding rarely occurs on loans or other financial instruments. For example, a mortgage loan typically has monthly, or semi-annual compounding, while credit card interest is applied daily in most cases.
How to find the effective interest rate? - nominal vs. effective interest rate
The best way to illustrate the difference between nominal vs. effective interest rate is to take a real-world example. Let's say you have 10,000 dollars that you would like to invest for your retirement.
You have two options:
- Deposit in a bank that offers a 3 percent annual rate compounded monthly; or
- Place it in an investment fund that offers the same annual rate but is compounded daily.
With which option would you be better off?
To answer this question, you must convert the annual rates of each scenario into effective interest rates.
So, how to find effective interest rate in this case? By applying the effective interest rate formula, the two scenarios result in the following effective interest rates:
EIR = (1 + 0.03 / 12)12 − 1 = 3.0416%
EIR = (1 + 0.03 / 365.242)365.242 − 1 = 3.0453%
The investment fund's higher effective interest rate suggests that you would earn more interest in that case. You may think that the small difference is irrelevant. Still, it can result in large differences in your investment's future value in the longer-term. If you are curious how, try out our savings goal calculator, where you can follow the long-term progress of your savings.
As you can see by now, expressing the nominal annual rate in effective interest rate provides a useful way to compare the effective costs or earnings of different loans or return rates in investments where the compounding differs.
How to use the effective interest rate calculator?
To run this effective interest rate calculator, you need to set the below parameters, and you will receive your results immediately:
- Annual interest rate - The nominal interest in a year;
- Periodic rate - The charged rate by a lender or paid by a borrower each period. In our effective interest rate calculator, the period refers to the compounding frequency, which coincides with the payment period;
- Compounding frequency - The number of times compounding occurs in a year; and
- Effective interest rate (EIR).
advance mode, you can find the following additions that you can use to compute future or present value with the given effective interest rate:
- Initial balance; and
- Final balance.