Equivalent Interest Rate Calculator - Convert Interest Rates Between Compounding Frequencies
Equivalent Interest Rate Calculator
Conversion Results
What Is the Interest Rate Conversion Formulas?
1. Effective Annual Rate (APY) Formula
The Effective Annual Rate represents the actual annual rate of return taking into account compounding:
For Discrete Compounding:
APY = (1 + r/n)n - 1
Where:
- r = nominal annual interest rate (as a decimal)
- n = number of compounding periods per year
For Continuous Compounding:
APY = er - 1
Where:
- r = nominal annual interest rate (as a decimal)
- e = Euler's number (≈ 2.71828)
2. Converting Between Compounding Frequencies
To convert from one compounding frequency to another:
Step 1: Calculate the Effective Annual Rate using the input compounding frequency
Step 2: Convert to the desired compounding frequency:
rnew = nnew × [(1 + APY)1/nnew - 1]
Where:
- rnew = nominal rate with new compounding frequency
- nnew = new number of compounding periods per year
- APY = effective annual rate from Step 1
3. Periodic Interest Rate
Periodic Rate = (1 + APY)1/n - 1
This represents the interest rate per compounding period.
Example 1: Converting APR to APY
Scenario: A credit card has an APR of 18% compounded monthly.
Calculation:
APY = (1 + 0.18/12)12 - 1 = 0.1956 = 19.56182%
Result: The effective annual rate (APY) is 19.56182%, which is higher than the stated 18% APR.
Example 2: Comparing Different Compounding Frequencies
Scenario: Compare 5% interest with different compounding frequencies:
- Annual: APY = 5.00%
- Quarterly: APY = 5.09453%
- Monthly: APY = 5.11619%
- Daily: APY = 5.12675%
- Continuous: APY = 5.12711%
Insight: More frequent compounding increases the effective rate, but the difference diminishes as frequency increases.
References
Government and Regulatory Sources
- Federal Reserve - APR and APY Explained
- FDIC - Understanding Deposit Interest
- CFPB - Understanding APR
- OCC - Treasury Department Interest Rate Information
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