Applications Involving Percents

Learning Objectives

  • Solve percent change and interest problems
    • Calculate discounts and markups using percent
    • Calculate interest earned or owed
    • Read and interpret data from pie charts as percents

Percent Change

Percents have a wide variety of applications to everyday life, showing up regularly in taxes, discounts, markups, and interest rates. We will look at several examples of how to use percent to calculate markups, discounts, and interest earned or owed.

Example

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off of the $220 original price.

The example video that follows shows how to use the percent equation to find the amount of a discount from the price of a phone.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

[latex]\begin{array}{c}10\%\,\,\text{of}\,\,220=0.1\cdot220=22\\20\%\,\,\text{of}\,\,220=0.2\cdot220=44\end{array}[/latex]

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

Interest

When a person takes out a loan, most lenders charge interest on the loan. Interest is a fee or change for borrowing money, typically a percent rate charged per year. We can compute simple interest by finding the interest rate percentage of the amount borrowed, then multiply by the number of years interest is earned.

Simple Interest Equation

[latex]I=p\cdot{r}\cdot{t}[/latex]

Where:

I is the interest paid

p is the principal—the original amount of money borrowed

r is the interest rate, a per-year rate, written as a decimal

t is the time of the loan, expressed in years or portions of a year

Example

Treasury Notes (T-notes) are bonds issued by the federal government to cover its expenses. Suppose you obtain a $1,000 T-note with a 4% annual rate, with a maturity in 2 years. How much interest will you earn?

In the following video, you are shown how to find how much interest is earned on a specified investment amount.

Example

A friend asks to borrow $240, offering to repay you $250 in 1 month. What annual interest rate is this equivalent to?

The example video that follows shows how to determine the annual simple interest rate.

Pie Charts

Circle graphs, or pie charts, represent data as sections of the circle (or “pieces of the pie”), corresponding to their percentage of the whole. Circle graphs are often used to show how a whole set of data is broken down into individual components.

Here’s an example. At the beginning of a semester, a teacher talks about how she will determine student grades. She says, “Half your grade will be based on the final exam and 20% will be determined by quizzes. A class project will also be worth 20% and class participation will count for 10%.” In addition to telling the class this information, she could also create a circle graph.

image

This graph is useful because it relates each part—the final exam, the quizzes, the class project, and the class participation—to the whole.

Example

If the total number of points possible in the class is 500, how many points is the final exam worth?

In the following video, an example of using a pie chart to determine a percent of a whole is shown.

Summary

When solving application problems with percents, it is important to be extremely careful in identifying the percent, whole, and amount in the problem. Once those are identified, use the percent equation to solve the problem. Write your final answer back in terms of the original scenario.