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# How to calculate an effective annual interest rate

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Matters of interest may not be interesting to many. Many people panic when it comes to complex financial jargon and acronyms. Nonetheless, if you’re the kind of business that extends credit, an understanding of how interest rates are calculated is essential. Indeed, if you run the kind of business that uses credit (which you almost certainly do), it’s also important to understand. Here, we’ll look at how to calculate an effective annual interest rate (EAR) so that you can better understand the interest that’s payable (or incoming) on the credit that you offer and use.

## What is an effective annual interest rate?

In order to better understand the real-terms effects of interest on our businesses, we need to take compounding into account. Whenever interest rates are advertised (nominal rates), compounding is not taken into account. But unless we do this ourselves, we can be left with inaccurate cash flow projections, and the potential for missed or late payments that may incur additional charges and further compromise our liquidity.

Simply put, the EAR is the interest that is paid back in real terms on any loan, credit card or other debt that you extend or use. It’s what you use to calculate your earnings on the credit you extend to your customers or your real-terms liability to your creditors.

### Understanding the EAR formula

Although there is a useful Effective Annual Interest Calculator that can automate the process for you, it’s important to get to know the formula for yourself. It requires you to understand two variables. The nominal annual interest rate that’s advertised (which we’ll refer to as r) and the number of periods within which interest (i) is compounded. Since this is usually measures in months, we’ll refer to this as m

Thus, the formula to calculate EAR (which we’ll refer to as i) looks like this:

The more compounding periods you have, the more you can expect your EAR to increase. So quarterly compounding produces higher returns than compounding every six months, while monthly compounding makes more than quarterly. Some creditors even compound daily.

Of course, if you’re not that mathematically inclined, this formula may be tricky to contextualise. So let’s look at an illustrative example.

## An example of an effective annual interest rate

Let’s say you need a new piece of equipment for your company. You know that this piece of equipment will cost you \$5,000 but you don’t have enough liquidity to cover that cost without disrupting your cash flow. So, you start shopping around for loans.

Bank A offers a nominal interest rate of 10% compounded monthly. Bank B offers a nominal interest rate of 10.1% compounded every 6 months. That 0.1% may seem negligible. But which is really the better offer?

Now that we know the formula, we can work it out.

• EAR = (1 + (nominal rate / number of compounding periods)) ^ (number of compounding periods) − 1

• For Bank A, this would be: 10.47% = (1 + (10% / 12)) x 12 − 1

• For Bank B, this would be: 10.36% = (1 + (10.1% / 2)) x 2 − 1

So, although Bank B may have a slightly higher nominal interest rate, it has a lower EAR than Bank A because it compounds fewer times over the course of the year. While this difference may only result in a saving of \$5.80 per year for a \$5,000 loan, if you needed to borrow substantially more, the difference can really add up!

If you’re interested in finding out more about calculating an Effective Annual Interest Rate, then get in touch with the financial experts at GoCardless. Find out how GoCardless can help you with ad hoc payments or recurring payments.

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