### Learning Outcomes

- Calculate simple interest earned given time, rate, and principal
- Calculate principal given interest earned and rate
- Calculate interest rate given principal and interest earned

Do you know that banks pay you to let them keep your money? The money you put in the bank is called the **principal**, [latex]P[/latex], and the bank pays you **interest**, [latex]I[/latex]. The interest is computed as a certain percent of the principal; called the **rate of interest**, [latex]r[/latex]. The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable for time, [latex]t[/latex], represents the number of years the money is left in the account.

### Simple Interest

If an amount of money, [latex]P[/latex], the principal, is invested for a period of [latex]t[/latex] years at an annual interest rate [latex]r[/latex], the amount of interest, [latex]I[/latex], earned is

[latex]I=Prt[/latex]

where

[latex]\begin{array}{ccc}\hfill I& =& \text{interest}\hfill \\ \hfill P& =& \text{principal}\hfill \\ \hfill r& =& \text{rate}\hfill \\ \hfill t& =& \text{time}\hfill \end{array}[/latex]

Interest earned according to this formula is called simple interest.

The formula we use to calculate simple interest is [latex]I=Prt[/latex]. To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information by listing all four variables and filling in the given information.

### example

Find the simple interest earned after [latex]3[/latex] years on [latex]\text{\$500}[/latex] at an interest rate of [latex]\text{6%.}[/latex]

Solution

Organize the given information in a list.

[latex]\begin{array}{ccc}\hfill I& =& ?\hfill \\ \hfill P& =& \text{$500}\hfill \\ \hfill r& =& \text{6%}\hfill \\ \hfill t& =& \text{3 years}\hfill \end{array}[/latex]

We will use the simple interest formula to find the interest.

Write the formula. | [latex]I=Prt[/latex] |

Substitute the given information. Remember to write the percent in decimal form. | [latex]I=\left(500\right)\left(0.06\right)\left(3\right)[/latex] |

Simplify. | [latex]I=90[/latex] |

Check your answer. Is [latex]\text{\$90}[/latex] a reasonable interest earned on [latex]\text{\$500}[/latex] in [latex]3[/latex] years? | |

In [latex]3[/latex] years the money earned [latex]18\text{%}[/latex]. If we rounded to [latex]20\text{%}[/latex], the interest would have been [latex]500(0.20)[/latex] or [latex]\text{\$100}[/latex]. Yes, [latex]\text{\$90}[/latex] is reasonable. | |

Write a complete sentence that answers the question. | The simple interest is [latex]\text{\$90}[/latex]. |

### try it

In the next example, we will use the simple interest formula to find the principal.

### example

Find the principal invested if [latex]\text{\$178}[/latex] interest was earned in [latex]2[/latex] years at an interest rate of [latex]\text{4%.}[/latex]

### try it

Now we will solve for the rate of interest.

### example

Find the rate if a principal of [latex]\text{\$8,200}[/latex] earned [latex]\text{\$3,772}[/latex] interest in [latex]4[/latex] years.