Difference Between APR and EAR

APR vs EAR

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-true’ interest rate for each year.

Illustrating the difference

If, for instance you have an annual APR of 12% and your deposit compounds quarterly, then you will earn 3% each quarter, meaning that for a deposit of $100 you will have $103 at the end of the first quarter. Then for the second quarter you will earn 3% on $103 which will earn you $106.09 as your balance at the end of the second quarter. After four quarters, that is at the end of the year, your earned interest will be $12.55.

The mathematical representation for that is FV = (Investment) x ((1 + i) ^ n), where i is the decimal interest rate per compounding period, n is the number of the periods and FV is the future value of the amount that earns interest at i. in the above example, this would be $112.55 = $100 x (1.03 ^ 4). The difference between the future value and the investment is the interest. Therefore, for a quarterly compounding, a 12% APR is equivalent to a 12.55% EAR.

Any APR can be converted to an EAR using the rate per compounding period and the number of compounding periods in a year. EAR= ((1 + i) ^ n) ‘“ 1. So, if monthly compounding rate is 1% for 12% APR, then EAR will be (1.01)^12 – 1 = .1268 = 12.68%.

So if you have an investment choice of 12% APR and 12.3% EAR then from the examples it is clear that the 12% APR is better, given risks and other factors are constant. The important thing to note is the rate being quoted, whether APR or EAR or any other so that a comparison can be made from the alternatives.

Summary:
1. APR is nominal annual percentage rate while EAR is effective percentage of interest rate.
2. APR can be converted to EAR using EAR= ((1 + i) ^ n) ‘“ 1 but the reversal is not true.
3. At the same percentage rate, APR gives slightly better returns than EAR, factors being constant.
4. APR is simple interest per year minus a fee while EAR is compound interest plus a fee calculated across the year.

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