Equivalent Rate Calculator
Convert interest rates between different compounding frequencies
Calculate Equivalent Rate
The stated annual interest rate before compounding
Current compounding frequency
Desired compounding frequency
Equivalent Rate Results
Formula used: i = q × [(1 + r/m)^(m/q) - 1]
Calculation: 4 × [(1 + 0%/12)^(12/4) - 1]
Conversion: Monthly → Quarterly
Initial Rate
Periodic Rate: 0.0000%
Frequency: Twelve times per year
Equivalent Rate
Periodic Rate: 0.0000%
Frequency: Four times per year
Rate Analysis
Example Calculation
Loan Rate Conversion
Original: 5% monthly compounding
Convert to: Quarterly compounding
Formula: i = 4 × [(1 + 0.05/12)^(12/4) - 1]
Calculation Steps
1. i = 4 × [(1 + 0.004167)³ - 1]
2. i = 4 × [1.012578 - 1]
3. i = 4 × 0.012578
Result: 5.0311% quarterly
This maintains the same effective annual rate.
Rate Conversion Tips
Equivalent rates maintain the same effective annual return
Higher frequency usually requires higher nominal rate
Use for comparing products with different terms
Essential for accurate financial modeling
Understanding Equivalent Rates
What are Equivalent Rates?
Equivalent rates are different nominal interest rates that, when compounded at different frequencies, produce the same effective annual rate (AER). This allows you to compare financial products with different compounding terms on an equal basis.
Why Use Equivalent Rates?
- •Compare loans or investments with different payment schedules
- •Convert between monthly, quarterly, and annual rates
- •Ensure accurate financial calculations and modeling
- •Make informed decisions about financial products
Equivalent Rate Formula
i = q × [(1 + r/m)^(m/q) - 1]
- i: Equivalent interest rate
- r: Nominal annual interest rate
- m: Initial compounding frequency
- q: New compounding frequency
Annual Equivalent Rate (AER)
AER = (1 + r/m)^m - 1
The effective annual rate shows the true yearly return after compounding.
Key Concepts
Nominal Rate
The stated annual rate before considering compounding
Compounding Frequency
How often interest is calculated and added to principal
Effective Rate
The actual annual return considering compounding effects
Equivalent Rate Examples
| Original Rate | Original Frequency | New Frequency | Equivalent Rate | AER |
|---|---|---|---|---|
| 5.00% | Monthly (12) | Quarterly (4) | 5.0311% | 5.1162% |
| 6.00% | Quarterly (4) | Monthly (12) | 5.9704% | 6.1364% |
| 4.50% | Semi-annual (2) | Annual (1) | 4.5506% | 4.5506% |