Effective Interest Rate (EIR) is an important tool to understand your actual return on investment against a stated annual interest rate (also known as the nominal rate) and it can be different from stated interest rate due to the effect of compounding.
It’s fascinating how the stated annual interest rate can differ from the actual return due to compounding. The Effective Interest Rate (EIR) or Annual Equivalent Rate (AER) takes into account the impact of compounding periods, which can lead to a higher return than the nominal rate suggests.
When interest compounds more frequently than annually—like monthly or quarterly—the actual return on your investment increases. The EIR provides a clearer picture of this, showing how much interest you’ll effectively earn in a year considering the frequency of compounding.
For instance, if your bank manager says you’re getting a 10% return compounded monthly, the EIR will be higher than 10% because interest is being added to your balance each month, and you then earn interest on the interest.
Formula
Effective Interest Rate = (1+i/n)^n-1
Where
i = stated interest rate
n = Number of compounding periods
Example:
Bank is offering interest @ 10% compounded monthly on an investment of $ 1000.
Required: Calculate Effective Interest Rate
Effective Interest Rate = [(1+10%/12)^12]-1 = 10.47%
Let’s verify this will actual calculation table below:
| Month | Opening Balance ($) | Monthly Interest @ 10% | Closing Balance ($) |
| 1 | 1000 | 8.3 | 1008.3 |
| 2 | 1008.3 | 8.4 | 1016.7 |
| 3 | 1016.7 | 8.5 | 1025.2 |
| 4 | 1025.2 | 8.5 | 1033.8 |
| 5 | 1033.8 | 8.6 | 1042.4 |
| 6 | 1042.4 | 8.7 | 1051.1 |
| 7 | 1051.1 | 8.8 | 1059.8 |
| 8 | 1059.8 | 8.8 | 1068.6 |
| 9 | 1068.6 | 8.9 | 1077.5 |
| 10 | 1077.5 | 9 | 1086.5 |
| 11 | 1086.5 | 9.1 | 1095.6 |
| 12 | 1095.6 | 9.1 | 1104.7 |
| Total Interest | 104.7 |
It is evident that actual return is 10.47% with interest of $104.7 on monthly compounding against the stated interest rate of 10%.
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