Why the APR Quoted by Your Credit Card Issuer Is Misleading

Time and again, on this blog, we have stressed the importance of paying off your balance before your due date. The primary reason behind this advice is that unless you do so, you run the risk of paying exorbitant rates of interest.

When you apply for a credit card, the issuing company indicates the APR (Annual Percentage Rate) that you may be subject to. This can vary anywhere between 9.99% and 30% - even higher. What’s worse is that the APR doesn’t reflect the actual interest you will be charged. In this article, we discuss why the interest rate you end up paying when carrying a balance is higher than the quoted APR.

To start with, you should be aware that the APR on your card is usually a variable rate. More often than not, it is the prime rate plus some percentage. So as the prime rate varies, your APR varies too. The APR quoted to you is mostly the daily interest rate on a certain date (let’s call this “r”) multiplied by the number of days in the year, usually 365. Thus APR = r*365. 

The actual annual rate, or in other words Effective Annual Rate (R), is the annual interest rate effective as of the date picked to compute APR.

Let’s take an example where you have a $100 balance on your card, and let’s assume that the daily interest rate for the next 365 days is the same (r). For each passing day, your daily balance gets charged an amount equal to the balance multiplied by the daily interest rate. So, after the first day, your new balance will become:

100+100*r=100*(1+r)

After the second day it will be:

100*(1+r)*(1+r)=100*(1+r)^2

This way, after 365 days your balance will be:

100*(1+r)^365

Since we called Effective Annual Rate as R, balance after 365 days can also be quoted as:

100+100*R=100*(1+R)

From the two equations above, we get

100*(1+r)^365 = 100*(1+R)

That is, R = (1+r)^365-1

So, while Effective Annual Rate (R) = (1+r)^365-1,

APR = r*365

So, if the APR is quoted as 20%, the effective daily rate, r=20%/365=0.0548%.

Thus, the Effective Annual Rate (R) = (1+0.0548%)^365-1=22.1%, which is 2.1% higher than the APR!

In other words, on a balance of $100, you would have to pay $22.10 as interest, and not $20 as implied by the APR.

Whether or not you were able to follow all the calculations above, the takeaway is that the interest charged by a credit card issuer on your outstanding balance is always greater than the quoted APR. Since the APR itself is usually so high to begin with, it is in your best interest to avoid carrying a balance on your card as much as possible.

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