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Nominal Interest Rate Formula

Before starting with the nominal interest rate formula, let us recall what the Nominal interest rate means. It refers to the interest rate before taking inflation into account. Nominal may also refer to the stated or advertised interest rate on a loan, without taking into account any fees or compounding of interest. Let us study the nominal interest rate formula using solved examples in the following section.

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What Is Nominal Interest Rate Formula?

Here are the nominal interest rate formulas. You can note that the formula is different for the small values of i. The general formula for nominal interest rate can be expressed as,

1 + R = (1 + r)(1 + i)

For small values of i, the formula can be rewritten as,

R = r + i

Effective Interest Rate (or Effective Annual Rate) can be calculated using the following formula:

Effective Annual rate (E.A.R.) = (1 + R/n)^n - 1

where

  • R is the nominal interest rate per period
  • r is the real interest rate
  • i is the inflation rate
  • n is the number of compounding periods

Let us see the applications of the nominal interest rate formula in the following section.

 

Solved Examples using Nominal Interest Rate Formula

 

  1. Example 1: Ramit's credit card has a nominal interest rate of 20%, compounded monthly, find the effective annual rate. 

    Solution. 

    To find: Effective annual rate

    Given:

    Nominal interest rate on credit card = 20%

    R = 20/100 = 0.20

    Using the nominal interest rate formula,

    Effective Annual Rate (E.A.R.) = (1 + R/n)^n - 1 = (1 + 0.20/12)^12 - 1 = (1.0167)^12 - 1 = 1.219 - 1 = 0.2198

    E.A.R. = 21.98%

    Answer: Effective Annual Rate (E.A.R.) is 21.98%

  2. Example 2: Given that the real interest rate is 4% and the nominal interest rate is 7%. What is the expected value of the inflation rate using the nominal interest rate formula?

    Solution.

    To find: Expected value of inflation rate

    Given:

    Real interest rate = 4% = 0.04

    Nominal interest rate = 7% = 0.07

    We know,

    1 + R = (1 + r)(1 + i)

    1 + 0.07 = (1 + 0.04)(1 + i)

    1.07 = 1.04 + 1.04i

    i = 0.03/1.04 = 0.0288

    Inflation rate = 2.88 %

    Answer: The inflation rate is 2.88%.

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