What Is APR? (Annual Percentage Rate)
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Annual Percentage Rate
APR, or Annual Percentage Rate, is a rate charged per year on an amount of money that is borrowed as a loan or invested which factors in associated fees in addition to the interest rate.
It is designed to give a more accurate estimate of the total cost of a loan or investment than considering the interest rate alone would.
When taking out a loan, there are three main factors that affect the total cost of the loan.
The principal is the initial amount given as a loan.
The interest rate, also called the nominal interest rate to emphasize the distinction from annual percentage rate, is the rate at which the balance of the loan will increase over time.
Lastly, there are usually a set of fees associated with taking out the loan, such as closing costs, origination fees, or insurance fees.
As a general rule, the APR of a loan is higher than the nominal interest rate.
This would only not be the case if a loan has no additional fees at any point in its lifetime.
Because the nominal interest rate of a loan can therefore be misleading, the Truth in Lending Act requires by law that all consumer lenders, such as credit card companies, disclose the APR of their loans, even though they are also allowed to advertise the nominal interest rate.
How to Calculate APR
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To understand how APR is calculated, let’s say that you were to take out a loan of $10,000 at 10% interest, with a term of 10 years that will be paid back at the end of the term.
That would make your annual interest expenses $1,000 per year.
Let’s also assume your bank has included fees associated with the loan totalling $500.
To get the APR of this loan, you need to add the cost of the fees to the total amount in interest paid.
Spread across a 10 year period, the additional $500 charge is divided by 10, which is $50 per year.
$50 is 0.5% of the $10,000 loan, adding 0.5% to the annual percentage rate.
Therefore, the annual percentage rate is 10% + 0.5% = 10.5%.
APR vs EAR
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While APR is a more accurate estimation of the total cost of a loan, it is limited because it only considers a simple interest rate.
If the interest compounds on a smaller time frame than annually (such as monthly or semi-annually), the actual interest paid will be higher than the APR advertised.
Factoring in compounding interest that happens within a year gives you a loan’s EAR, or Effective Annual Rate (sometimes also called APY, or Annual Percentage Yield).
Let’s say that you take out a loan of $100 on January 1st with a nice, even APR of 12%, compounded monthly.
This means that your APR interest rate per month is 1%, but that interest will compound monthly.
At the end of January, your loan balance will be $100 plus 1% of $100, or $101.
The next month, the interest will be 1% of $101, so at the end of February your balance will be $102.01, and so on.
Here is how an APR of 12% compounded monthly would be converted to EAR in mathematical form:
12% / 12 = 1%
1% / 100 = 0.01
1 + 0.01 = 1.01
1.01^12 = 1.1268
1.1268 – 1 = .1268 * 100 = 12.68%
Here are the steps written out:
To get the EAR of a loan, first convert the APR to a monthly interest rate.
In our example, that value is 12% divided by 12 which equals 1% per month.
You then take the interest levied per period and divide by 100 to get a decimal (0.01).
Next, add 1 to that number to get 1.01.
Then raise that new number (1.01) to the power of n, where n is the number of periods per year (in this case, there are 12 months per year so 1.01^12 = 1.1268).
Subtract 1 from that value and convert the number back to a percentage (1.1268 – 1 = .1268 = 12.68%).
In this example, the EAR is 12.68% which is 0.68% higher than 12%.
Fun fact: A .68% difference between APR and EAR (which is the actual amount paid) on a loan of $10,000 compounded over a 20 year period comes out to an extra $12,414.22 in total interest paid ($96,462.93 vs $108,877.16).
This is why it’s important to understand the difference between the interest advertised (usually APR) and the actual amount paid (usually EAR).
Unfortunately, the type of person in this predicament aren’t generally the ones reading about the difference between APR and EAR.
As a helpful rule of thumb, most credit card companies use an APR compounded monthly, whereas most mortgages use an APR that is calculated on an annual basis and is therefore the same as EAR.
If you are carrying credit card debt, your APR is already high to begin with, but your EAR is even greater than the stated APR, plus you may be charged additional fees for late payments!
Here is how to remember interest rate, APR, and EAR:
Interest rate is the interest on the principal borrowed which does not factor in additional fees, and is usually stated annually.
Annual Percentage Rate (APR) is the interest plus additional fees, stated as a percentage.
This is stated annually and therefore does not factor in rates compounded on smaller time frames (such as monthly).
Effective Annual Rate (EAR) factors in additional fees and whether the rate is compounded on a smaller time frame.
An APR is needed to compute the EAR.