# Why Does Effective Annual Rate Matter?

It is common practice for lenders to state interest rates in annual percentage rate (APR). APR expresses how much interest you pay if interest was calculated on an annual basis (i.e. after 12 months), but this is not the case for most credit products. For example, interest on credit cards and student loans are calculated daily, even though you pay at the end of the month. For those that have student loans and log into your  account to see how much you owe, you will see your daily interest charge.

Let’s look at a simple example. You have a credit card balance of \$5,000 at 20% on Jan 1. A simple APR calculation at the end of the year would show \$6,000 owing (\$5,000 + \$1,000 interest at the 20%). But in order for this to be true it would mean that the lender only charges interest once a year (i.e. on Dec 31), which is not the case. Interest charges on credit cards are determined daily and billed monthly.

So you need to compare apples to apples. Convert the APR of 20% to how often the lender calculates interest on the debt. So for credit cards daily interest charge would be 20% / 365 days = 0.0547% per day on a \$5,000 balance. Here is an example of how interest would be charged on the first 3 days of a \$5,000 credit card debt.

 Date Beginning Bal. Calculation (Interest Amount+ Principal) Ending Balance Jan 1 \$5000 (\$5000 X 0.0547%) + \$500 \$5002.74 Jan 2 \$5002.74 (\$5002.74 X 0.0547%) +\$5002.74 \$5005.48 Jan 3 \$5005.48 (\$5005.48 X 0.0547%) + \$5005.48 \$5008.22

You get the idea.

What the APR does not tell you is the compounding interest effect on the debt. In other words, it assumes a charge once a year instead of daily, weekly, monthly etc.

Although 20% is being used, when divided over 365 days and compounded daily, against the balance of the debt, you see that one would owe more than \$6,000 at the end of the year.

To compare apples to apples, you need to factor in how often debt is being compounded. This is called the effective annual rate (EAR). Luckily, you don’t have to go through this grueling exercise; there are financial calculators that can give you the effective annual rate.

The effective annual rate for a credit card with 20% interest compounded daily is actually 22.133%. Multiply this by \$5,000, it would give a better representation of how much is owed at the end of the year; \$6,106.65 (\$5,000X 22.133% + \$5,000).

The difference between these two amounts is not substantial \$106.65 (\$6,106.65-\$6,000) for one year, but extend this over multiple years and you can see the impact.

At a minimum it is important to understand this distinction so you remain an informed consumer and investor. This is why compound interest works great for savers, not for borrowers. This is also why lenders almost always state interest rates in annual percentage rate (APR), not effective annual rate (EAR).

Albert Einstein said it best:

### “Compound interest is the 8th wonder of the world. He who understand it earns it. He who doesn’t, pays it”.

Categories: Debt, Savings

### 3 replies ›

1. I love the piece but doubt the quote. http://www.snopes.com/quotes/einstein/interest.asp

Like

2. Great post. Love your Einstein quote at the end.

Like