Effective Interest Rate Calculator
Calculate the true cost of borrowing or the real return on investments
Formulas Used
Periodic Interest Rate
Periodic Rate = Nominal Rate / Compounding Frequency
The interest rate applied each compounding period.
Effective Annual Rate (Discrete Compounding)
EAR = (1 + (Nominal Rate / n))ⁿ – 1
Where n is the compounding frequency per year. This calculates the actual annual rate when compounding is considered.
Effective Annual Rate (Continuous Compounding)
EAR = eʳ – 1
Where r is the nominal rate and e is Euler’s number (~2.71828). Used when interest compounds continuously.
After-Tax Rate
After-Tax Rate = Nominal Rate × (1 – Tax Rate)
or
After-Tax Rate = Nominal Rate × (1 + Tax Rate) for deductible interest
The tax-adjusted rate depending on whether it’s investment income (taxed) or loan interest (deductible).
Future Value
FV = P × (1 + (r/n))^(n×t)
Where P is principal, r is nominal rate, n is compounding frequency, and t is time in years.
About Effective Interest Rate
What is Effective Interest Rate?
The effective interest rate (EIR), also called the equivalent annual rate (EAR), is the actual interest rate that an investor earns or a borrower pays in a year after accounting for compounding. Unlike the nominal interest rate, the EIR considers how often compounding occurs.
Why is it Important?
Financial institutions often advertise nominal rates which can be misleading. The effective rate gives you the true cost of a loan or the real return on an investment. Comparing effective rates allows for accurate comparisons between different financial products with different compounding periods.
Tax Considerations
For accurate financial planning, it’s important to consider tax implications. Investment interest is typically taxable, while mortgage and some loan interest may be tax-deductible. The after-tax effective rate provides the most realistic picture of your actual return or cost.
Common Applications
- Comparing loans with different compounding periods
- Evaluating investment returns with different compounding frequencies
- Understanding the true cost of credit cards or mortgages
- Financial planning and retirement calculations
- After-tax return analysis for investments
- Tax planning for deductible interest expenses