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#### 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

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 = PRN

, where P is the principal, R is the annual interest rate in decimal form, and N 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 = PRN = (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.