Effective annual interest rate versus nominal interest rate. It’s one of the things to look at when choosing where to open a savings account.
Bank A offers you a 6% nominal annual interest rate, and so does Bank B. At Bank A, the interest is credited to your account annually, at Bank B monthly. Does that make any difference? 12 times 0.5% interest equals 6% per year, right? The difference is the compounding effect of monthly interest versus yearly interest.

⏱️TIMESTAMPS⏱️
00:00 Effective vs nominal interest rate
00:35 Effective annual interest rate example
02:25 Effect of compounding
02:51 EAR on credit card debt
03:43 General rule effective rate vs nominal rate
04:04 Effective annual interest rate formula

Here’s how things work in your savings account at Bank A. You start the year with $10,000 in your account. If there are no deposits or withdrawals, that account balance stays the same throughout the year, until the 1st of January of the next year when $600 of interest (6% of $10,000) is credited to your account.

At Bank B, things work differently. You start the year with the same $10,000 in your account. On a monthly basis, 0.5% interest on the previous month’s balance gets credited.
On February 1st, your balance is $10,050. Your original $10,000 plus 0.5% interest on $10,000.
On March 1st, your balance is $10,100.25. The February 1st balance of $10,050 plus 0.5% interest on that balance. Another way to think about this is, is that you once again get $50 of interest on $10,000, but you also get 25 cents of interest on the $50 of interest that you earned in January. That’s what compounding is all about: interest on interest.
On January 1st of the next year, you have $10,616.78 in your account at Bank B. Through the effect of monthly compounding, you earned an extra $16.78 in interest at Bank B versus Bank A. At Bank A, the nominal rate is 6%, and the effective annual interest rate is also 6%. At Bank B, the nominal rate is 6%, while the effective annual interest rate is slightly higher at 6.17%.

Let’s now take a look at the effective annual interest rate or #EAR of your credit card debt at Bank C. The nominal annual rate is 12 * 2% = 24%. What is the effective annual interest rate? If there are no new charges to the credit card and you are not paying off any debt, then the original balance of $10,000 quickly grows over the months, to $12,682.42. If we had used the nominal interest rate of 24% on an annual basis, that balance would have been $12,400, so through the effect of monthly compounding you owe an extra $282.42 in interest. In other words, while the nominal rate is 24%, the #effectiverate is 26.8%!

Here's the general rule on nominal rate vs. effective annual interest rate or EAR. The higher the interest rate, and the more frequent the compounding periods, the bigger the difference between nominal and effective rate.

Once you understand the effective annual interest rate formula, you will see why.

In the EAR formula, i is the nominal annual interest rate, and n is the number of compounding periods. EAR equals open parentheses 1 + i/n close parentheses, to the power n, and all of that minus one. In our earlier example of the savings account at Bank B, the nominal interest rate was 6%, and the number of compounding periods 12 (monthly). Plug those values into the formula. Calculate the various elements of the EAR formula, knowing that 0.5% in percentage terms equals 0.005 in absolute terms. The outcome is an EAR of 6.17%, in other words a delta between the nominal annual interest rate and the effective annual interest rate of 0.17%-points.
In our credit card example, we reached an effective rate of 26.8% based on monthly compounding. What is the EAR based on a nominal rate of 24% and 365 compounding periods, in other words daily compounding. Plug those values into the formula, and calculate the various elements of the EAR formula. i divided by n gets very small if you divide by 365, but the compounding to the power 365 makes up for it. The outcome of the calculation is an EAR of 27.11%, in other words a delta between the nominal annual interest rate and the effective annual interest rate of 3.11%-points or 311 basispoints as it is called in the world of banking. If you want to experiment some more, then have a go at the EAR in Excel!

Philip de Vroe (The Finance Storyteller) aims to make accounting, finance and investing enjoyable and easier to understand. Learn the business and accounting vocabulary to join the conversation with your CEO at your company. Understand how financial statements work in order to make better investing decisions. Philip delivers #financetraining in various formats: YouTube videos, livestreams, classroom sessions, and webinars. Connect with me through Linked In!

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