Equivalent Rate Calculator
Calculate equivalent rates across different compounding frequencies. Find the Annual Equivalent Rate (AER) and compare how the same effective rate appears with different compounding periods.
Equivalent Rate Results
All Frequencies Comparison
Results will appear here after calculation
Rate Insights
Most Common: Monthly compounding
Highest Effective: Daily compounding
Simplest: Annual compounding
Tip: AER allows fair rate comparisons
Understanding Equivalent Rates and AER
Equivalent rates allow you to compare interest rates or yields that have different compounding frequencies. The Annual Equivalent Rate (AER) standardizes all rates to an annual basis with the same compounding effect, making accurate comparisons possible.
How Equivalent Rates Work
To find equivalent rates between different compounding frequencies:
Rate2 = (1 + Rate1/n1)^(n1/n2) - 1
Where: n1 = original compounding periods, n2 = target compounding periods
Annual Equivalent Rate (AER)
AER converts any nominal rate to an equivalent annual rate with the same compounding effect. It's calculated as:
AER = (1 + r/n)^n - 1
Where: r = nominal rate, n = compounding frequency per year
Why Equivalent Rates Matter
- Fair Comparisons: Compare rates with different compounding
- Accurate Decisions: Choose best investment or loan option
- Regulatory Compliance: Required disclosure in many countries
- Financial Planning: Better understanding of true costs/returns
- Risk Assessment: Evaluate different financial products
Compounding Frequency Impact
| Compounding | Periods/Year | 10% Nominal Rate | AER |
|---|---|---|---|
| Annually | 1 | 10.00% | 10.00% |
| Semi-Annually | 2 | 9.76% | 10.00% |
| Quarterly | 4 | 9.65% | 10.00% |
| Monthly | 12 | 9.57% | 10.00% |
| Daily | 365 | 9.53% | 10.00% |
Applications of Equivalent Rates
- Savings Accounts: Compare different compounding frequencies
- Investment Products: Evaluate mutual funds and ETFs
- Loan Comparisons: Compare different credit products
- Bond Yields: Standardize different bond yields
- Financial Planning: Make informed investment decisions
Regulatory Requirements
Many financial regulators require the disclosure of AER to ensure consumers can make informed decisions.
- UK Financial Services: AER required for savings products
- EU Consumer Credit: AER disclosure mandatory
- Australian Banking: AER required for deposit products
- Canadian Regulations: AER disclosure for loans and savings
Practical Examples
Savings Account Comparison
Two savings accounts with different compounding:
- Account A: 4.5% compounded monthly
- Account B: 4.6% compounded quarterly
- AER A: (1 + 0.045/12)^12 - 1 = 4.60%
- AER B: (1 + 0.046/4)^4 - 1 = 4.68%
- Account B offers better return
Loan Comparison
Two loan options with different compounding:
- Loan A: 12% compounded monthly
- Loan B: 12.2% compounded quarterly
- AER A: (1 + 0.12/12)^12 - 1 = 12.68%
- AER B: (1 + 0.122/4)^4 - 1 = 12.89%
- Loan A is cheaper despite lower nominal rate
Common Mistakes
- Comparing Nominal Rates: Different compounding makes them incomparable
- Ignoring AER: Can lead to wrong financial decisions
- Assuming Annual = AER: Only true for annual compounding
- Mixing Products: Compare similar products (savings with savings)
- Forgetting Fees: AER doesn't include fees and charges
Tip: Always use AER when comparing financial products with different compounding frequencies. The nominal rate alone can be misleading and lead to poor financial decisions. AER provides a standardized way to compare the true annual cost or return of different products.