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Effective Interest Rate

Key Takeaways:

  • The Effective Annual Interest Rate (EAR) is the total interest associated with a loan or investment.
  • The effective rate takes compounding into effect.
  • The EAR will always be higher than the stated annual interest rate.

When you take out a loan, whether it’s a personal loan, payday loan, mortgage, or auto loan, you will see various interest rates, including the stated interest rate and annual percentage rate.

You seldom see the Effective Annual Interest Rate (EAR), despite its importance.

So, what is effective interest rate and how does it work?

How Effective Interest Rate Works

The effective interest rate is the total interest cost associated with a loan.

All loans have compound interest, meaning the bank includes the previous month’s accrued interest when calculating your next month’s interest.

The effective rate takes this into consideration and expresses it as a rate that is generally slightly higher than the stated interest rate but lower than the APR.

How to Calculate Effective Interest Rate

The effective rate of interest is one of the easier financial calculations to make, but you still need an in-depth equation to figure it out.

The effective interest rate formula is:

r = (1 + i/n)^n – 1

The “r” is your effective interest rate, “i” is the stated interest rate in its decimal format (3% is 0.03), and “n” is the number of times the interest compounds in a year.

Generally, the “n” will be a 12 because most loans compound monthly, but, in some rare cases, it can also be daily, weekly, or continuously.

An example:

Let’s say you have a $100,000 loan with a 3% stated interest rate that compounds monthly, here is how to calculate the effective interest rate:

r = (1 + 0.03/12)^12 – 1

That would equal a 3.04% effective interest rate.

While that may seem insignificant and trivial, this can be a helpful tool when comparing loan offers that are virtually identical terms.

The table below shows how effective annual rates change with compounding:

Interest RateSemi-AnnualQuarterlyMonthlyDaily
1%1.0025%1.0038%1.0046%1.0050%
2%2.0100%2.0151%2.0184%2.0201%
3.%3.0225%3.0339%3.0416%3.0453%
4%4.0400%4.0604%4.0742%4.0808%
5%5.0625%5.0945%5.1162%5.1267%
10%10.2500%10.3813%10.4713%10.5156%
15%15.5625%15.8650%16.0755%16.1798%
20%21.0000%21.5506%21.9391%22.1336%
25%26.5625%27.4429%28.0732%28.3916%
30%32.2500%33.5469%34.4889%34.9692%
35%38.0625%39.8676%41.1980%41.8830%
40%44.0000%46.4100%48.2126%49.1498%

Why the Effective Rate Is Important

The effective rate of interest determines an investment’s true return or a loan’s true interest rate.

The annual interest rate and effective interest rate can differ significantly due to compounding. The effective rate can help you figure out the bcrest loan rate or which investment offers the best return.

When compounding is taken into consideration, the EAR will always be higher than the stated annual interest rate.

As an example, if you deposit $10,000 into a savings account with a stated interest rate of 12%, compounding monthly, the effective rate will be around 12.69%, as the following table shows:

MonthBalanceInterest EarnedEnding Balance
1$10,000.00$100$10,100.00
2$10,100.00$101.00$10,2501.00
3$10,201.00$102.01$140,303.01
4$10,303.00$103.03$10,406.03
5$10,406.00$104.06$10,510.06
6$10,510.00$105.10$10,615.10
7$10,615.00$106.15$10,721.15
8$10,721.00$107.21$10,828.21
9$10,829.00$108.29$10,937.29
10$10,973.00$109.73$11,082.73
11$11,046.00$110.46$11,156.46
12$11,157.00$111.57$11,268.57

The change in interest rate from the start where the balance was at $10,000, to the end where the balance is $11,268, is the effective interest rate (12.683%).

Even though the bank stated a 12% interest rate, your investment grew by 12.68%.

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    Lorien is the Country Manager for Financer US and has a strong background in finance and digital marketing. She is a fintech enthusiast and a lover of all things digital.

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    Last Updated: May 1, 2022

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