Nominal rates and effective rates are two different ways of expressing the interest rate on a loan or investment. Nominal rates are the stated or quoted rates that do not account for inflation or compounding. Effective rates are the actual rates that account for both inflation and compounding, and therefore reflect the true cost or return of borrowing or investing.
For example, suppose you deposit $100 into a bank account that pays a nominal interest rate of 10% per year, compounded quarterly. This means that every quarter, you will earn 10% / 4 = 2.5% interest on your balance. After one year, your balance will be:
$100 x (1 + 0.025)^4 = $110.38
The effective interest rate is the annualized rate that gives you the same result as the nominal rate with compounding. In this case, the effective interest rate is:
(1 + 0.025)^4 – 1 = 0.1038 or 10.38%
The effective interest rate is higher than the nominal interest rate because of the compounding effect. The more frequently the interest is compounded, the higher the effective interest rate will be.
To compare different loans or investments, it is important to use the effective interest rate rather than the nominal interest rate, as it gives a more accurate picture of the actual cost or return. You can also use the effective interest rate to calculate the present value or future value of a cash flow, using the standard formulas for the time value of money.
Basic Theory:
Nominal Rate:
The nominal interest rate, often referred to as the stated or annual rate, represents the percentage of interest on an annual basis before considering compounding.
Effective Rate:
The effective interest rate, also known as the annual equivalent rate (AER) or annual percentage yield (APY), takes compounding into account. It reflects the actual interest earned or paid over a year, considering the frequency of compounding.
Procedures:
Calculating Nominal Rate in Excel:
Suppose the nominal rate is given as 
, and the number of compounding periods per year is 
. The formula in Excel is:
Nominal Rate = R
Calculating Effective Rate in Excel:
If the nominal rate is and compounding occurs times per year, the effective rate can be calculated using the formula:
Effective Rate = (1 + R/n)^n - 1
Scenario:
Let’s consider a scenario where a loan is offered at a nominal rate of 8% per annum, compounded quarterly (four times a year).
- Nominal Rate (): 8%
- Compounding Periods (): 4
Excel Calculation:
Nominal Rate = 8%
Effective Rate = (1 + 8%/4)^4 - 1
Excel Table:
| Nominal Rate | Compounding Periods | Effective Rate |
|---|---|---|
| 8% | 4 | Formula Result |
Result:
After plugging in the values and performing the calculations in Excel, the effective interest rate is approximately 8.24%.
Other Approaches:
- Using the EFFECT Function:
In Excel, you can also use theEFFECTfunction to calculate the effective interest rate. For the scenario mentioned, the formula would be:
=EFFECT(8%, 4)
The result will be the same as the manual calculation.
- Data Table for Sensitivity Analysis:
Utilize Excel’s data table feature to conduct a sensitivity analysis by changing the nominal rate and compounding periods. This provides a dynamic view of how different combinations affect the effective rate.
