# Nominal Interest Rate: Definition & Equation

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• 0:01 What Is Nominal Interest Rate?
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Lesson Transcript
Instructor: Shawn Grimsley
Understanding interest rates is a vital part of personal and business financial management. In this lesson, you'll learn about the nominal interest rate and how to calculate it from different perspectives. A short quiz follows the lesson.

## What Is the Nominal Interest Rate?

Interest is the money that a lender receives from a borrower in exchange for the borrower's use of the lender's money (called the principal). The nominal interest rate is the rate of interest that is reported on loan documents and investment accounts that are not adjusted for inflation. You should keep in mind, however, that a sophisticated lender takes the expected rate of inflation into account when determining the interest rate it will charge on a loan. Nevertheless, the expected inflation rate and the actual rate of inflation usually is not the same.

## How to Calculate the Nominal Interest Rate

Before we jump into calculating the nominal interest rate, let's start simple with the simple interest formula: I = PRT, where I = interest, P = principal, R = interest rate, and T = time.

Now, let's do some algebraic operations to get the formula for finding the simple interest rate: R = I/PT, where I = interest, P = principal, R = interest rate, and T = time. For example, imagine you took out a loan one year ago that is now due. The principal amount of the loan is \$10,000 and you owe \$1,000 in interest. What is the annual nominal interest rate on the loan?

Here's our formula with these numbers plugged in: R = 1,000/(10,000)(1). Note that since unit of time in this question is a year, we use 1. If the unit of time was monthly, we would use 12. If it were daily, you would use either 365 or 360, depending upon how a year is defined in the loan documents (360 is often used):

R = 1,000/10,000

R = .10 (you can convert this decimal to a percent by multiplying by 100)

R = .10 * 100

R = 10%

Now, let's turn to the nominal interest rate from the view of the lender. Remember that a smart lender will factor in the expected rate of inflation to ensure the desired rate of return (profit). Here's an equation that a lender may use to calculate the nominal interest rate it wishes to charge a borrower: nominal interest rate = real interest rate + expected inflation rate.

The real interest rate is the interest rate adjusted for inflation. The real interest rate should equal the nominal interest rate on the day the loan is given because inflation has not had an effect yet. A lender will then increase the real interest rate by adding the expected inflation rate to it. It's important to emphasize that this calculation does not take into account actual inflation, but rather expected inflation. It's impossible to take into account the effect of actual inflation because it has not occurred yet.

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