Interest Rate Converter
Category: Asset-Class ConvertersConvert between Annual Percentage Rate (APR) and Effective Annual Rate (EAR) to understand the true cost of loans and investments
Rate Conversion
Comparison
APR vs. EAR over Different Compounding Frequencies
APR to EAR Conversion Table
| Compounding | APR: 5.00% | Effective Rate | Difference |
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Conversion Formulas
APR to EAR Formula:
Where n is the number of compounding periods per year. For continuous compounding, the formula is: EAR = eAPR - 1
EAR to APR Formula:
Where n is the number of compounding periods per year. For continuous compounding, the formula is: APR = ln(1 + EAR)
Understanding Interest Rate Conversions
When analyzing loans, investments, or financial products, understanding the difference between APR and EAR is crucial for making informed decisions. These rates may seem similar, but they represent interest in fundamentally different ways.
Annual Percentage Rate (APR)
- Simple interest rate: Does not account for compounding
- Nominal rate: The stated interest rate without considering frequency of compounding
- Required for loans: In many countries, lenders must disclose APR by law
- Linear calculation: Easy to calculate but doesn't show the true cost over time
Effective Annual Rate (EAR)
- Compound interest rate: Accounts for the effects of compounding
- True annual cost: Reflects the actual amount paid/earned over a year
- Comparison tool: Allows accurate comparison between different compounding frequencies
- Always higher: EAR is always higher than APR (except for annual compounding)
Practical Examples
A credit card with 18% APR compounded monthly has an EAR of 19.56%. This means you'll actually pay 19.56% interest over a year if you don't pay your balance in full each month.
A savings account offering 2% APR with daily compounding has an EAR of 2.02%. The difference is small but becomes more significant with higher interest rates or longer time periods.
An investment promising 8% APR compounded quarterly has an EAR of 8.24%. When comparing investments, using EAR provides a more accurate picture of your actual returns.
Asset-Class Converters Tools:
What this calculates
Conversion between nominal, effective and continuously compounded rates.
- Formula
effective = (1 + nominal ÷ n)ⁿ − 1; continuous = e^r − 1- Worked example
- 6% nominal compounded monthly is (1 + 0.06/12)¹² − 1 = 6.17% effective.
- When to use it
- Whenever comparing rates quoted on different compounding conventions.
- Common mistake
- Comparing a monthly-compounded rate with an annual one directly. The headline numbers look close while the effective rates differ.