Nominal Interest Rate v. Effective Interest Rate
Guess what? You’re paying more on your credit card purchases than the interest rate listed in your terms. But wait, don’t go grabbing for the pitchforks yet – the usual credit card issuer trickery isn’t afoot. Rather, it’s just the simple math of compounding interest working this time. According to the Truth in Lending Act, lenders are only required to disclose the nominal APR – that is the interest rate plus any fees (membership fees, application fees, origination fees, etc). The nominal APR, also referred to as the stated interest rate will always be lower than what you actually pay over a year’s time. That’s called the effective interest rate.
Why is the Effective Interest Rate More?
To understand the effective interest rate requires just a wee bit of math. Let’s say that you are taking out a 1 year loan for $10,000 from the bank at 12%. You might assume that you’d end up paying $1,200 in finance fees for a total of $11,200. After all, 12% of $10,000 is $1,200 right? Right. But you’re wrong about how much you’ll pay in the end. The $1,200 paid out in interest would be true if you only paid interest once after the loan term was up. In that case, you could just use the equation you learned in high school math: Interest (I) = Principle (P) times Interest Rate (R) times Time (T).
In reality, you’ll likely be charged interest several times a year. Let’s say you had to pay interest once a quarter. First, you’d calculate the periodic rate. In this case, you’d take the APR and divide it by the amount of payment periods. 12% divided by 4 is 3% per quarter. So, on March 1st you’d be charged 3% of $10,000. The principle becomes $10,300. In June, they’d tack on an additional 3% to $10,300 for a total of $10,609. By September you’re at $10,927. At the end of the year, you owe $11,255. That’s $55 more than you thought. That’s because, even though your stated interest rate was 12%, because you had 4 compounding periods, your effective interest rate was actually 12.551%.
Effective Interest and Deferred Payments
Looking at these figures, you might think: “Hey, wait a second. What kind of lender would have compounding periods but wouldn’t require me to make any payments during that whole time?” The answer: department store credit cards. Anytime you walk into a Macy’s or Dillard’s or Boscov’s, you’ll likely be bombarded by signs offering “NO PAYMENTS FOR 12 MONTHS” or “ZERO INTEREST FOR A FULL YEAR!” It seems like a sweet deal at first, but most of these offers come with a catch.
Zero interest on purchases is just one of the many so-called convenient offers from credit card companies that actually end up costing you. If you read the asterisk or ask for more information, you’ll likely find out that the interest isn’t merely forgiven during those 12 months, rather it’s quietly accumulating in the background at the interest rate that the card will have once your “promotional period” is over. Let’s say that after 12 months, your balance goes automatically to 25%. If you didn’t pay off your balance with the deferred interest before the end of the promotional period, it will all get tacked on immediately. Say, for instance, that you bought a $500 item and didn’t pay it off after 12 months. Assuming that the interest was added on once a month, you’ll owe around $640.35. That’s an effective interest rate of 28.07%. On the other hand, if you would’ve made the minimum monthly payment on the item (let’s say 5% of the balance) instead of deferring the interest, you would have made payments of $256 in payments and have about $350 left to pay. That’s about a $33 difference at the 12 month mark (and that number will climb the longer you take to pay it off). So in reality, these zero interest for 12 months promotions translate to “buy now, pay extra later.”
Calculating Effective Interest Rate
When weighing out the true cost of a credit card payment, you may want to take some time to figure out the effective interest rate first. To do so, use the following formula
Effective interest rate = (1 + I/n) to the nth power minus 1
Here, interest is I while n is the number of compounding periods (in most cases, the number is 12). Or if that’s too difficult, why not just use this Effective Annual Interest Rate Calculator. To calculate how much you’ll really be paying (assuming that you don’t pay down the principle), simply plug the effective annual interest rate into the principle. Or just use the Credit Card Calculator.
As you can see, the nominal interest rate only tells you so much about how much you are paying. Because of compounding interest, you can end up paying significantly more for your purchases, especially if you defer your interest for a period of time.
Photo by ralphunden.
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Thanks for the explanation! The part about how making payments on the couch during the promo period instead of waiting until the end was helpful :)
You lost me at this part though: “So, on March 1st you’d be charged 3% of $10,000. The principle becomes $10,300. In June, they’d tack on an additional 10% to $10,300 for a total of $10,609.”
I’m confused about the 10 percent. The $309 increase from March to June is only a 3 percent increase…?
Oops – typo. Thanks for pointing that out, Dee.