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How to Find Simple Interest Rate: Definition, Formula & Examples

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  • 0:02 What is Simple Interest?
  • 0:47 Simple Interest Formula
  • 2:34 Simple Interest Example
  • 3:56 Maturity Value
  • 8:01 Lesson Summary
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Lesson Transcript
Instructor: Norair Sarkissian
When we borrow a certain sum of money over a period of time, we agree that we will pay it back, along with a fee, known as the interest owed. Similarly, when we invest a sum of money in a savings account, the account earns us interest. This lesson will show you how to calculate a certain type of interest called simple interest.

What is Simple Interest?

Simple interest is a type of interest that is applied to the amount borrowed or invested for the entire duration of the loan, without taking any other factors into account, such as past interest (paid or charged) or any other financial considerations. Simple interest is generally applied to short-term loans, usually one year or less, that are administered by financial companies. The same applies to money invested for a similarly short period of time.

The simple interest rate is a ratio and is typically expressed as a percentage. It plays an important role in determining the amount of interest on a loan or investment. The amount of interest charged or earned depends on three important quantities that we will examine next.

Simple Interest Formula

Sarah needs to borrow $2,000 in order to buy furniture. She's approved for two different loans. Loan One allows her to borrow $2,000 now, provided that she pay off the loan by returning $2,200 exactly one year from the day that she borrows the money. Loan Two offers her $2,000 upfront as well, with a similar loan period of one year, at an annual interest rate of 7%. Which is the better deal for Sarah?

The amount borrowed or invested is called the principal. Using the example above, when Sarah borrows $2,000 to buy furniture, we say that the principal is $2,000.

It's customary for financial institutions to quote a quantity called the interest rate as a percentage. This interest rate represents a ratio of the principal borrowed or invested. Typically, this interest rate is given as a percentage per year, in which case it is called the annual interest rate. For example, if we borrow $100 at an annual rate of 5%, it means that we will be charged 5% of $100 at the end of the year, or $5.

The loan period or duration is the time that the principal amount is either borrowed or invested. It is usually given in years, but in some cases, it may be quoted in months or even days. If that is the case, we need to perform a conversion from a period given in months or days, into years.

The simple interest formula allows us to calculate I, which is the interest earned or charged on a loan. According to this formula, the amount of interest is given by I = Prt, where P is the principal, r is the annual interest rate in decimal form, and t is the loan period expressed in years.

Example

The second offer that Sarah has received is to borrow a principal amount P = $2,000, at an annual rate of 7%, over t = 1 year. The rate r must be converted from a percentage into decimal form, which means that we divide the percentage value 7% by 100 to get r = 0.07.

We now calculate the amount of interest Sarah would be charged if she accepts the loan offer just described:

I = Prt = (2,000)(0.07)(1) = $140.

Following our example, we determined that if Sarah accepts the second loan, the interest that she will owe the bank is $140. So, how much would Sarah have to pay the bank in order to pay off her debt? She would have to pay back the money she borrowed, or the principal, which is $2,000, and she would have to pay the bank the interest we calculated, in which I = $140. Thus, she will owe the bank $2,000 + $140, which equals $2,140. We note that this is still less than the $2,200 Sarah would have to pay if she accepts Loan One. Obviously, Loan Two is the better choice.

Future of Maturity Value

The total amount we would need to pay back when we take a loan is called the future value of the loan. Another name for future value is maturity value. The future value, A, of a loan is given by the equation A = P + I. When we invest a principal amount (P), the future value (A) will represent the total amount we will have at the end of the loan period after simple interest is applied.

Using the interest formula I = Prt, we can derive a formula for the future value, since A = P + Prt, or after factoring out P on the right hand side, A = P(1 + rt).

Example 1

Lilya borrows $300 from her local bank at an annual interest rate of 3.25% to be paid back in six months. How much interest will she pay at the end of the loan?

Solution

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