Need business and finance help to better understand APR and EAR

Business & Finance
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APR (annual percentage rate) gives us the interested rate paid or earned in one year without compounding. It is calculated by taking the interest rate per period and multiply it by the number of periods when compounding occurs during the year.

EAR (effective annual rate) is the annual compounded rate that produces the same return as the nominal or stated rate.

The difference is APR is simple interest per year minus a fee while EAR is compound interest plus a fee calculated across the year.

Nov 20th, 2015

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APR refers to the nominal annual percentage of rate while EAR refers to the effective percentage of rate or effective APR. These are descriptions of the annualized interest rate rather than the monthly rate calculated on a loan or mortgage. The terms carry legal jurisdictions in some countries but speaking generally, APR is the simple interest rate per year while EAR is the compound interest rate plus a fee calculated across a year. APR is calculated as the rate for payment period, multiplied by the number of payment periods in a year. However, the precise definition of EAR varies in each given jurisdiction, depending on the type of fees that may apply such as monthly service charges, participation fees or loan originating fees. EAR is called the mathematically-trueinterest rate for each year. EAR( effective annual rate) is more relevant because EAR is the compound interest rate which considers the cost of interest also.

For example: 

Essentially, the effective annual return accounts for intra-yearcompounding, and the stated annual return does not.

The difference between these two measures is best illustrated with an example. Suppose the stated annual interest rate on a savings account is 10%, and say you put $1,000 into this savings account. After one year, your money would grow to $1,100. But, if the account has a quarterly compounding feature, your effective rate of return will be higher than 10%. After the first quarter, or first three months, your savings would grow to $1,025. Then, in the second quarter, the effect of compounding would become apparent: you would receive another $25 in interest on the original $1,000, but you would also receive an additional $0.63 from the $25 that was paid after the first quarter. In other words, the interest earned in each quarter will increase the interest earned in subsequent quarters. By the end of the year, the power of quarterly compounding would give you a total of $1,103.80. So, although the stated annual interest rate is 10%, because of quarterly compounding, the effective rate of return is 10.38%.

That difference of 0.38% may appear insignificant, but it can be huge when you're dealing with large numbers. 0.38% of $100,000 is $380! Another thing to consider is that compounding does not necessarily occur quarterly, or only four times a year, as it does in the example above. There are accounts that compound monthly, and even some that compound daily. And, as our example showed, the frequency with which interest is paid will have an effect on effective rate of return.


Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 20th, 2015

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Nov 20th, 2015
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