The table below shows the year-by-year growth of the investment and the cumulative effective rate.
| Year | Starting balance | Interest earned | Ending balance | Effective rate to date (%) |
|---|
Effective Interest Rate and Compounding Calculator
Understanding the Effective Interest Rate
The effective interest rate, also called the effective annual rate (EAR), represents the true yearly cost or return of money once compounding is taken into account. While lenders and financial institutions often quote a nominal rate, the effective rate can be significantly higher when interest is compounded multiple times per year.
From nominal rate to effective annual rate
The nominal rate is the stated yearly percentage that does not by itself reflect how frequently interest is added to the balance. When interest is compounded, each compounding period earns interest not only on the original principal but also on previously accumulated interest. The relationship between the nominal rate \( i_{\text{nom}} \), the number of compounding periods per year \( m \) and the effective annual rate \( i_{\text{eff}} \) is:
\[ i_{\text{eff}} = \left( 1 + \frac{i_{\text{nom}}}{m} \right)^{m} - 1 \]
When the compounding frequency increases, the effective annual rate also increases, even though the nominal rate remains unchanged. This is why it is essential to compare loans and investments using the effective rate rather than the nominal rate alone.
How this effective interest rate calculator works
This calculator lets you input a nominal annual interest rate, a compounding frequency, the number of years and an initial principal amount. It then computes the effective annual rate using the formula above and applies compounding over the selected time horizon to produce a detailed schedule of balances.
The core calculations include:
- Effective annual rate: \[ i_{\text{eff}} = \left( 1 + \frac{i_{\text{nom}}}{m} \right)^{m} - 1 \]
- Total number of compounding periods: \[ N = m \times t \] where \( t \) is the number of years.
- Future value of the investment: \[ FV = PV \times \left( 1 + \frac{i_{\text{nom}}}{m} \right)^{N} \] where \( PV \) is the initial principal.
The year-by-year table uses the same compounding relationship to track the starting balance, interest earned and ending balance for each year. The cumulative effective rate after each year is calculated as:
\[ i_{\text{eff, cumulative}} = \frac{\text{Ending balance}}{PV} - 1 \]
Using the results for financial decisions
By comparing effective rates across different products, you can make informed decisions about savings accounts, certificates of deposit, bonds and loans. For borrowers, a higher effective rate means a higher true cost of debt. For investors, a higher effective rate represents stronger growth, but it may also be associated with higher risk.
When evaluating alternatives, consider:
- Compounding frequency and how it changes the effective rate.
- Investment horizon and the effect of time on cumulative growth.
- Principal size and how small differences in rate compound into large differences in value.
Limitations and practical considerations
The calculator assumes a constant nominal rate and a fixed compounding frequency over the entire period, with no additional contributions or withdrawals. Real-world products may apply fees, minimum balances or tiered rates that modify the effective return. Still, the mathematical framework used here provides a reliable baseline for understanding how compounding transforms a nominal rate into a true effective rate.
Use the effective interest rate as a standardized benchmark whenever you compare savings, investment or borrowing options. It helps you align different offers on a common scale and avoid being misled by attractive but incomplete nominal rate figures.