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Theeffective interest rate (EIR),effective annual interest rate (EAR),annual equivalent rate (AER) or simplyeffective rate is the percentage ofinterest on aloan or financial product ifcompound interest accumulates in periods different than a year.[1] It is the compound interest payable annually inarrears, based on thenominal interest rate. It is used to compare the interest rates between loans with different compounding periods. In a situation where a 10% interest rate is compounded annually, its effective interest rate would also be 10%.[1]
The effective annual rate (EAR) expresses the equivalent annual interest if compounding occurs more than once per year. It is given by[1]
wherei is the nominal annual rate andn the number of compounding periods (e.g., 12 for monthly). For example, a nominal rate of 6% compounded monthly gives an EAR of 6.17%, since each month 0.5% is applied and after 12 months the growth factor is. The EAR rises with more frequent compounding.
| Nominal annual rate | Frequency of compounding | ||||
|---|---|---|---|---|---|
| Semi-annual | Quarterly | Monthly | Daily | Continuous | |
| 1% | 1.003% | 1.004% | 1.005% | 1.005% | 1.005% |
| 5% | 5.063% | 5.095% | 5.116% | 5.127% | 5.127% |
| 10% | 10.250% | 10.381% | 10.471% | 10.516% | 10.517% |
| 15% | 15.563% | 15.865% | 16.075% | 16.180% | 16.183% |
| 20% | 21.000% | 21.551% | 21.939% | 22.134% | 22.140% |
| 30% | 32.250% | 33.547% | 34.489% | 34.969% | 34.986% |
| 40% | 44.000% | 46.410% | 48.213% | 49.150% | 49.182% |
| 50% | 56.250% | 60.181% | 63.209% | 64.816% | 64.872% |
The primary difference betweenannual percentage rate (APR) and effective interest rate, is that the effective interest rate includes the compounding effect, while APR assumes the payee has paid off all interest on a loan each month.[2] Additionally, the APR method, depending on legal jurisdiction, reflects other factors that may effect the cost of a loan such as including fees that may be charged as a part of a loan. Effective interest is the standard in the European Union and many other countries, while APR is often used in the United States.[citation needed]
Annual percentage yield or effective annual yield is the analogous concept for savings or investments, such as acertificate of deposit. Since a loan by a borrower is an investment for the lender, both terms can apply to the same transaction, depending on the point of view. For azero-coupon bond such as aUS treasury bill, anannual effective discount rate may be specified instead of an effective interest rate, because zero coupon bonds trade at a discount from their face values.[3]
In accountancy, the term effective interest rate is used to describe the rate used to calculate interest expense or income under theeffective interest method.[citation needed] This is not the same as the effective annual rate, and is usually stated as an APR rate.
