Nominal vs Effective Interest Rate: TVM Guide
In Time Value of Money, compounding frequency affects the actual return. Let's compare Nominal and Effective interest rates.
head-to-Head Comparison
| Basis | Nominal Interest Rate | Effective Interest Rate |
|---|---|---|
| Compounding Effect | Stated interest rate that does not account for intra-year compounding. | Actual interest rate earned/paid, accounting for the effect of compounding during the year. |
| Value | Always lower than or equal to the effective interest rate. | Always higher than or equal to the nominal interest rate (higher with more compounding periods). |
| Calculation Formula | Stated rate (usually denoted as $r$ or $i$) | $$E = (1 + i/m)^m - 1$$ (where $m$ is compounding periods per year) |
The 'Continuous Compounding' Value
As the compounding frequency approaches infinity (continuous compounding), the effective interest rate formula converges to: $$E = e^r - 1$$. The gap between nominal and effective rate reaches its maximum here.
Common Ground (Similarities)
- Both measure the cost of borrowing or rate of investment return.
- Both are expressed as a percentage per annum.
Test Your Understanding
Q1: If interest is compounded quarterly, how does the effective rate compare to the nominal rate?
Effective rate is lower
Effective rate is higher ✅
Both are equal
Cannot be determined
Explanation: Compounding quarterly adds interest-on-interest four times a year, pulling the effective rate above the nominal rate.