Effective Annual Rate (EAR) Calculator
Convert nominal interest rates to effective annual rates by adjusting for daily, monthly, or quarterly compounding. Reveal the true cost of lending.
About
Financial products often advertise a nominal rate that looks attractive on paper but fails to account for the frequency of compounding. Lenders and banks use different compounding schedules that can significantly alter the actual interest paid or earned over a year. This discrepancy creates a hidden cost for borrowers and a hidden benefit for savers. The Effective Annual Rate (EAR) standardizes these figures to provide a single transparent percentage for comparison.
Accuracy is critical when evaluating loans or high-yield savings accounts. A nominal difference of partial percentage points can translate into substantial sums when compounded daily rather than annually. This tool calculates the precise EAR based on your input parameters and highlights the delta between the advertised rate and the real mathematical obligation.
Formulas
The calculation uses the standard compound interest formula to adjust the nominal rate r based on the number of compounding periods n.
Where r is the decimal nominal rate and n is the compounding frequency per year.
Reference Data
| Compounding Frequency | Periods per Year (n) | Nominal Rate (r) | Effective Rate (EAR) | Difference |
|---|---|---|---|---|
| Annually | 1 | 10.00% | 10.000% | 0.000% |
| Semi-Annually | 2 | 10.00% | 10.250% | 0.250% |
| Quarterly | 4 | 10.00% | 10.381% | 0.381% |
| Monthly | 12 | 10.00% | 10.471% | 0.471% |
| Bi-Weekly | 26 | 10.00% | 10.496% | 0.496% |
| Weekly | 52 | 10.00% | 10.506% | 0.506% |
| Daily | 365 | 10.00% | 10.516% | 0.516% |
| Continuous | ∞ | 10.00% | 10.517% | 0.517% |