Effective Nominal Interest Rates

Overview

Engineering reference data for Effective Nominal Interest Rates in economics.

Key Formulas

Present Value

$PV = \frac{FV}{(1+r)^n}$

Discount a future value to present.

Net Present Value

$NPV = \sum_{t=0}^{n} \frac{C_t}{(1+r)^t}$

Sum of discounted cash flows.

Compound Interest

$FV = PV(1+r)^n$

Future value with compound interest.

Variables

Calculating Nominal and Effective Interest Rates

The relationship between nominal and effective interest rates depends on the time period and the number of sub-periods. Below are the formulas and examples for converting between them.

Nominal Interest Rate: For a period with $n$ sub-periods and an effective interest rate $i_e$ per sub-period, the nominal interest rate $i$ is: $i = (1 + i_e)^n - 1$

Effective Interest Rate: Given a nominal interest rate $i_n$ for a period, the effective interest rate $i_e$ per sub-period is: $i_e = (i_n + 1)^{1/n} - 1$

Examples:

• With an effective monthly interest rate of $1\%$ ($i_e = 0.01$), the nominal annual interest rate is: $i = (1 + 0.01)^{12} - 1 = 0.127 = 12.7\%$
• For a nominal annual interest rate of $10\%$, the effective monthly interest rate is: $i_e = (0.1 + 1)^{1/12} - 1 = 0.00797 = 0.797\%$

References

• Original Source