Percent Applications

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Overview

In the following section, we will look at three applications for percents: tax, discounts, and simple interest.

Sales Tax

Sales tax and commissions are an application of percents used in our everyday lives. The sales tax is a percent of the purchase price.

How much do you pay for sales tax when you shop in your city or state? Sales tax is added to the purchase price of an item. See the figure below.

Notice that the sales tax is determined by computing a percent of the purchase price.

To find the sales tax, we must convert the sales tax rate from a percent to a decimal number and multiply the purchase price by the sales tax rate. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost — what the customer pays.

Finding Sales Tax and Total Cost

1. Sales Tax = Tax Rate (as a decimal) • Purchase Price
2. Total Cost = Purchase Price + Sales Tax

Example 1: Cathy bought a bicycle in Washington, where the sales tax rate was 6.5% of the purchase price. What is the A) sales tax and B) total cost of a bicycle if the purchase price of the bicycle was $392?

A) To find the sales tax, we need to take the tax rate and convert it into a decimal. If we move the decimal two places to the left, we can convert 6.5% to the decimal 0.065.

Next, we will multiply the tax rate as a decimal by the purchase price. If we multiply 0.065 by 392, we get 25.48. This means the sales tax will be $25.48.

B) To find the total cost, we will need to add the purchase price with the sales tax. If we add $392 to $25.48, the total cost of the bicycle will be $417.48.

Example 2: Find A) the sales tax and B) the total cost: Kim bought a winter coat for $250 in St. Louis, where the sales tax rate was 8.2% of the purchase price.

A) To find the sales tax, we need to take the tax rate and convert it into a decimal. If we move the decimal two places to the left, we can convert 8.2% to the decimal 0.082.

Next, we will multiply the tax rate as a decimal by the purchase price. If we multiply 0.082 by 250, we get 20.5. This means the sales tax will be $20.50.

B) To find the total cost, we need to add the purchase price with the sales tax. If we add $250 to $20.50, the total cost of the bicycle will be $270.50.

Discount

Applications of discounts are common in retail settings. When you buy an item on sale, the original price of the item has been reduced by some dollar amount. The discount rate, usually given as a percent, is used to determine the amount of the discount. An amount of discount is a percent off the original price.

To determine the amount of a discount, we multiply the discount rate by the original price. We summarize the discount model in the box below.

Finding Discount and Sales Price

1. Discount = Discount Rate (as a decimal) • Original Price
2. Sale Price = Original Price – Discount

The sale price should always be less than the original price. In some cases, the amount of discount is a fixed dollar amount. Then, we just find the sale price by subtracting the amount of discount from the original price.

Example 3: Elise bought a dress that was discounted 35% off of the original price of $140. What was A) the amount of discount and B) the sale price of the dress?

A) Before we find the discount, we need to convert 35% into the decimal 0.35. Next, we will multiply 0.35 by the original price. If 0.35 • 140 = 49, then the discount for the dress is $49.

B) To find the sale price, we need to subtract original price by the discount. If 140 – 49 = 91, then the sale price of the dress is $91.

Example 4: Sergio bought a belt that was discounted 40% from an original price of $29. Find A) the amount of discount and B) the sale price.

A) Before we find the discount, we need to convert 40% into the decimal 0.4. Next, we will multiply 0.4 by the original price. If 0.4 • 29 = 11.6, then the discount for the belt is $11.60.

B) To find the sale price, we need to subtract original price by the discount. If 29 – 11.60 = 17.4, then the sale price of the belt is $17.40.

Poll

Solve Simple Interest Applications

Do you know that banks pay you to let them keep your money?

The money you put in the bank is called the principal, P, and the bank pays you interest, I. The interest is computed as a certain percent of the principal called the rate of interest, r. The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of a percent. The variable for time, t, represents the number of years the money is left in the account.

Equation for Simple Interest

I = Prt

where

I = interest
P = principal
r = rate (as a decimal)
t = time (as a year)

The formula we use to calculate simple interest is I = Prt. 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 1: Find the simple interest earned after 3 years on $500 at an interest rate of 6%.

Find the simple interest earned after 3 years on $500 at an interest rate of 6%. Let’s organize the given information in a list:

I = ?
P = $500
r = 6% = 0.06
t = 3 years

We will use the simple interest formula (I = Prt) to find the interest. If we substitute the given information, be sure not to forget to use the percent in decimal form. This looks like I = (500)(0.06)(3). If I = 90, this means the simple interest is $90 over 3 years.

Example 2: Nathaly deposited $12,500 in her bank account where it will earn 4% interest. How much interest will Nathaly earn in 5 years?

We are asked to find the interest, I. Organize the given information in a list:

I = ?
P = $12,500
r = 4% = 0.04
t = 5 years

Once again, we will use the simple interest formula (I = Prt) to find the interest. If we substitute the given information, be sure not to forget to use the percent in decimal form. This looks like I = (12500)(0.04)(5). If I = 2500, this means the simple interest is $2500 over 5 years.