© 2010 pearson prentice hall. all rights reserved. chapter 8 consumer mathematics and financial...

© 2010 Pearson Prentice Hall. All rights reserved.

CHAPTER 8

Consumer Mathematics and Financial Management

© 2010 Pearson Prentice Hall. All rights reserved. 2

§8.1, Percent, Sales Tax, and Income Tax


Learning TargetsI will express a fraction as a percent.I will express a decimal as a percent.I will express a percent as a decimal.I will solve applied problems involving sales tax and

discounts.I will compute income tax.I will determine percent increase or decrease.I will nvestigate some of the ways percent can be

abused.


Basics of Percent

• Percents are the result of expressing numbers as a part of 100.

• The word percent means per hundred.

Expressing a fraction as a percent:

1. Divide the numerator by the denominator.

2. Multiply the quotient by 100. This is done by moving the decimal point in the quotient two places to the right.

3. Add a percent sign.


Example 1: Expressing a Fraction as a Percent

Express as a percent.

Solution:

Step 1. Divide the numerator by the denominator.

5 ÷ 8 = 0.625

Step 2. Multiply the quotient by 100.

0.625 100 = 62.5

Step 3. Add a percent sign.

62.5%

Thus, = 62.5%.

8

5

8

5


Expressing a Decimal as a Percent

To express a decimal as a percent:

1. Move the decimal point two places to the right.

2. Attach a percent sign.


Example 2: Expressing a Decimal as a Percent

Express 0.47 as a percent.

Solution:

Thus, 0.47 = 47%.


Expressing a Percent as a Decimal Number

To express a percent as a decimal number:

1. Move the decimal point two places to the left.

2. Remove the percent sign.


Example: Express each percent as a decimal:

a. 19% b. 180%

Solution: Use the two steps.

a.

Thus, 19% = 0.19.

b. 180% = 1.80 or 1.8

Example 3: Expressing Percents as Decimals


Percent, Sales Tax, & Discounts

Many applications involving percent are based on the following formula:

Note that “is” implies equal to and “of” implies multiplication.

•We use this formula to determine sales tax collected by states, counties, cities on sales items to customers. Sales tax amount = tax rate item’s cost


Example 4: Percent and Sales Tax

Suppose that the local sales tax rate is 7.5% and you purchase a bicycle for $894.

a.How much tax is paid?

b.What is the bicycle’s total cost?

Solution:

a.Sales tax amount = tax rate item’s cost

7.5% $894 = 0.075 $894 = $67.05

The tax paid is $67.05.

b. Total Cost = $894.00 + $67.05 = $961.05

The bicycle’s total cost is $961.05.


Percent and Sales Price

• Businesses reduce prices, or discount, to attract customers and to reduce inventory.

• The discount rate is a percent of the original price.

Discount amount = discount rate original price.


Example 5: Percent and Sales Price

A computer with an original price of $1460 is on sale at 15% off.

a.What is the discount amount?

b.What is the computer’s sale price?

Solution:

a.Discount amount = discount rate original price

The discount amount is $219.


b. A computer’s sale price is the original price, $1460, minus the discount amount, $219.

Sale price = $1460 $219 = $1241

The computer’s sale price is $1241.

Example 5: Percent and Sales Price continued


Percent and Income Tax

Calculating Income Tax:

1. Determine your adjusted gross income:

2. Determine your taxable income:


3. Determine the income tax:



• The table shows tax rates, standard deductions, and exemptions for the four filing status categories.



Example: Calculate the income tax owed by a single woman with no dependents whose gross income, adjustments, deductions, and credits are given. Use the marginal tax rates from the table.

Example 6: Computing Income Tax

Single Woman with no dependents:

Gross income: $62,000

Adjustments: $4,000

Tax credit: $500

Deductions:

• $7500: mortgage interest• $2200: property taxes• $2400: charitable contributions• $1500: medical expenses not covered the insurance


Solution:

Step 1. Determine the adjusted gross income.

Adjusted gross income = Gross income – Adjustments

= $62,000 $4000

= $58,000

Percent and Income TaxExample Continued


Step 2. Determine taxable income.

We substitute $12,100 for deductions in the formula for taxable income.

Example 6 continued


Taxable income = Adjusted gross income – (Exemptions + Deductions)

= $58,000 – ($3500 + $12,100)

= $58,000 – $15,600

= $42,400

Step 3. Determine the income tax.

Income tax = Tax computation – Tax credits

= Tax Computation $500

Since the single woman taxable income is $42,400 she falls in the tax bracket of 25%.

Example 6 continued


• This means that she owes:

10% on the first $8025 of her taxable income, 15% on her taxable income between $8026 to $32,500, inclusive, and 25% on her taxable income above $32,550.

Example 6 continued


= 0.10 $8025 + 0.15 ($32,550 $8025) + 0.25 ($42,400 $32,550)

= 0.10 $8025 + 0.15 ($24,525) + 0.25 $9850

= $802.50 + $3678.75 + $2462.50

= $6943.75

We substitute $6943.75 for the tax computation in the formula for income tax.

Income tax = Tax computation – Tax credits

= $6943.75 $500

= $6443.75

Thus, the income tax owed is $6443.75.

Example 6 continued


Percent and Change

If a quantity changes, its percent increase or its percent decrease can be found as follows:

1. Find the fraction for the percent increase or decrease:

2. Find the percent increase or decrease by expressing the fraction in step 1 as a percent.

.amount original

decrease ofamount or

amount original

increase ofamount

Notice the denominator is the original amount in either case.


In 2000, world population was approximately 6 billion. The data are from United Nations Family Planning Program and are based on optimistic or pessimistic expectations for successful control of human population growth.

Example 7: Finding Percent Increase and Decrease

a. Find the percent increase in world population from 2000 to 2150 using the high projection data.

b. Find the percent decrease in world population from 2000 to 2150 using the low projection data.


Solution:

a. Use the data shown on the blue, high-projection, graph.

The projected percent increase in world population is 400%.

Example 7: Finding Percent Increase and Decrease continued

amount of increasePercent increase

original amount

30 6 24 4 400%

6 6


b. Use the data shown on the green, low-projection, graph.

The projected percent decrease in world population is 33⅓%.

%3

133

3

1

6

2

6

46

amount original

decrease ofamount decreasePercent

Example 7: Finding Percent Increase and Decrease continued


Example 9: Abuses of Percents

John Tesh, while he was still co-anchoring Entertainment Tonight, reported that the PBS series The Civil War had an audience of 13% versus the usual 4% PBS audience, “an increase of more than 300%.” Did Tesh report the percent increase correctly?

Solution: We begin by finding the actual percent increase.

The percent increase for PBS was 225%. This is not more than 300%, so Tesh did not report the percent increase correctly.

%22525.24

9

4

413

amount original

increase ofamount increasePercent

© 2010 pearson prentice hall. all rights reserved. chapter 8 consumer mathematics and financial...

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