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Principal Amount: Definition & Formula

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  • 0:00 What Is a Principal Amount?
  • 0:52 What About Interest?
  • 1:44 Principal Amount Formulas
  • 3:00 Compound Interest Formulas
  • 5:10 Lesson Summary
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Lesson Transcript
Instructor: Mia Primas

Mia has taught math and science and has a Master's Degree in Secondary Teaching.

In this lesson, you will learn the definition of principal amount. We will look at formulas and examples that will help you to calculate principal amounts of loans and accounts. You can then take a brief quiz to test what you learned.

What Is a Principal Amount?

Principal amount on a loan is the amount borrowed. To better understand, let's look at the story of John. When John bought his first car he didn't have enough money to pay for it in cash, so he had to take out a loan. He borrowed $7,500. According to the terms of the loan, John had to pay it off in five years with an interest rate of 10%. The initial amount that he borrowed, or the $7,500, is called the principal amount of the loan. Keep in mind that the principal amount applies to more than just loans. It can also apply to money that is invested or deposited into an account. For example, if you open a savings account with a $700 deposit, the principal amount is $700.

What About Interest?

Principal amount does not include interest, or a rate paid as a fee for borrowing money. To figure out the amount of interest John paid during the five years, you can use the simple interest formula, which is a formula to calculate interest paid only on the principal amount. This formula is:

principal1

or interest equals principal amount times interest rate times amount of time. Using this formula, you will find that the amount of interest on John's $7,500 loan was $3,750. So, at the end of five years, he would end up paying a total of $11,250. This does not include any additional fees that may apply.

Principal Amount Formulas

For John's loan, we were given the principal amount and used it to find the amount of interest. What if we already know the interest rate, amount of interest, and amount of time, but we need to find out the principal amount? We can rearrange the interest formula, I = PRT to calculate the principal amount. The new, rearranged formula would be P = I / (RT), which is principal amount equals interest divided by interest rate times the amount of time.

Let's try this out by finding the principal amount of a loan that has a total interest amount of $18,500 and an annual interest rate of 6.5% over 12 years.

To solve, we input the values into the equation, P = I / (RT). This gives us:

P = $18,500 / (0.065 * 12) = $23,718

The principal amount of the loan is $23,718.

Compound Interest Formulas

We can also use the principal amount and interest rate to find the compound interest, which is the total interest on both the principal and any accumulated interest not paid off within the repayment period. The compound interest formula is:

principal4

And if we already have the compound interest amount and need to find the principal amount, we can also rearrange this formula to suit our needs. The formula may seem complicated, but it's really just about plugging in numbers. Let's apply it to something other than loan amounts.

Say that our friend Maria has an investment account, and at the end of 7 years, the balance of the investment account is $33,818, which is the initial investment plus the interest. If the interest compounded annually at a rate of 2.5%, what is the principal amount?

First, we need to apply the values we have to the formula. We substitute $33,818 for A in our formula; that's the initial investment plus the interest. The rate is 2.5% over 7 years, so we substitute 0.025 for r and 7 for t. The interest is compounded annually, or one time per year, so we substitute 1 for n.


principal5


When we solve, we find that the principal amount of the investment is $28,450.

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