Calculation
The effective interest rate is calculated as if compounded annually. The effective rate is calculated in the following way, where r is the effective annual rate, i the nominal rate, and n the number of compounding periods per year (for example, 12 for monthly compounding):
For example, a nominal interest rate of 6% compounded monthly is equivalent to an effective interest rate of 6.17%. 6% compounded monthly is credited as 6%/12 = 0.005 every month. After one year, the initial capital is increased by the factor (1 + 0.005)12 ≈ 1.0617.
When the frequency of compounding is increased up to infinity the calculation will be:
The yield depends on the frequency of compounding:
| Nominal Rate | Semi-Annual | Quarterly | Monthly | Daily | Continuous |
|---|---|---|---|---|---|
| 1% | 1.002% | 1.004% | 1.005% | 1.005% | 1.005% |
| 5% | 5.062% | 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 effective interest rate is a special case of the internal rate of return.
If the monthly interest rate j is known and remains constant throughout the year, the effective annual rate can be calculated as follows:
Read more about this topic: Effective Interest Rate
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