1. Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved.

2. Percents and Their Applications
Chapter 6
Percents and Their Applications
Prepared by Dr. Elena Skliarenko
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved.

3. Percent and Their Applications#6
Percent and Their Applications
Learning Unit Objectives
LU6.1
Definition and Conversions
List the types of mortgages available
Utilize an amortization chart to compute monthly mortgage payments
Calculate the total cost of interest over the life of a mortgage
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved.

4. Percent and Their Applications#6
Percent and Their Applications
Learning Unit Objectives
LU6.2
Applications: Portion Formula
List the types of mortgages available
Utilize an amortization chart to compute monthly mortgage payments
Calculate the total cost of interest over the life of a mortgage
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved.

5. Percent and Their Applications#6
Percent and Their Applications
Learning Unit Objectives
LU6.3
Applications: Percent Change: Percent of Increase/Decrease
List the types of mortgages available
Utilize an amortization chart to compute monthly mortgage payments
Calculate the total cost of interest over the life of a mortgage
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved.

6. Percent and Their Applications#6
Percent and Their Applications
Learning Unit Objectives
LU6.4
Applications: Taxes
Goods and Services Taxes (GST)
Provincial Sales Taxes (PST)
Property Tax
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7. Bag of M&M’s Decimal Percent Color Fraction (hundredth) (hundredth)
Yellow % 55
Red %
Blue %
Orange %
Brown %
Green %
Total %
55 = 1
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8. Converting Decimals to Percents & Percents to Decimals
Move decimal point 2 places to the right, add zeros if necessary
.75
75% 5
500%
.35
2.5
35%
250%
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9. Rounding Percents = 5 13 %
38.46%
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved.

10. Converting Percents to Decimals
Drop the percent symbol and move the decimal point 2 places to the left. .8
.00.8
.8%
.008
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11. Converting Fraction Percents to Decimals
.50% =
1 % 2
.00.50
.0050
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved.

12. Converting Fractions to Percents
.10 = 1 10
.10.
10%
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13. Converting a Whole Percent to a Fraction
76 x 1
100
76% 76
100
Reduce to lowest terms 19 25
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14. Converting a Mixed or Decimal Percent to a Fraction1 2 32
65 x = 65
32.5%
Reduce to lowest terms 13
100
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15. Application of Percents - Portion Formula
Portion (P) = Base (B) x Rate (R)
Portion “is”
Base “of”
Rate “%”
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16. Solving for Portion
Sales of McDonalds drive-thru customers are 60% of total sales. Total sales are $1,600,000. What are the drive-thru sales?
Portion = Base x Rate
P = $1,600,000 x .60
P = $960,000
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17. Solving for Rate
Sales of McDonalds drive-thru customers are $960,000. Total sales are $1,600,000. What Percent of customers eat in the restaurant?
Rate = Portion
Base
R = $640, 000
$1,600,000
R = 40%
$1,600,000
- 960,000
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18. Solving for Base
Sales of McDonalds drive-thru customers are 60% of total sales. Sales of eat-in customers are $640,000. What are total sales?
Base = Portion
Rate
B = $640,000
.40
B = $1,600,000
eat in sales
Percent of customers that eat-in
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19. Rate of Percent Decrease
15 oz.
Rate = Portion
Base
Rate = 12 15
Amount of Decrease (P)
Original Weight (B)
.80 or 80%
Decrease
3 oz.
Original
New
Percent of Decrease (R)
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20. Rate of Percent Increase
$1,000
Rate = Portion
Base
Rate = $1,500
Original sales (B)
1.5 or 150%
Increase
$2,500
Original
New
Amount of Increase (P)
Percent of Increase (R)
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21. V Vo – Old/Initial value Rc – Percent change
Formula 6.3.1 V
Vo – Old/Initial value
Rc – Percent change
(Vn –Vo) – Amount of change (Increase or Decrease). If amount of change is positive then the quantity increases in size and percent change is also positive. If amount of change is negative, then the quantity decreases and percent change is also negative.
n – New/Final value
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22. Calculate the rate of percent decreases and increases
Base
Rate(Rc) = Portion
Initial (Old) number
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23. Sales Tax Taxes paid on certain goods and services
The sales tax percent is calculated by the state. Merchants collect funds and forward them to the respective government agencies
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24. In Canada there are two levels of government taxes, federal and provincial, on sales of goods and services to the final customers.
Federal Goods and Services Tax (GST)
Goods and Services Tax (GST) is a value added tax, which is levied by the federal government on nearly all goods and services in Canada. GST Payable is remitted to a special federal government authority, called Receiver General for Canada. Only educational, health and financial services are subject to exemption from GST.
Provincial Sales Tax (PST)*
 Provincial Sales Tax (PST) is levied on sales to the final customers and varies from province to province. Out of all Canadian provinces only Alberta and the Territories have exemptions from PST. In Prince Edward Island and in Quebec PST is calculated as a percent of sales price plus GST ( PST = PST% x (Sales Price + GST) ).
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25. PST rates are represented in the following table:
Alberta
British Colum-
bia
Manito- ba
North
West Terri-
tories
Nunavut
Ontario
PEI
Quebec
Saskat-
chewan
Yukon
Terri- 0% 7% 8%
10%
7.5% 6%
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26. Sales Tax
Compute sales tax and total price given the following information:
Selling price of computer $700
Shipping charge $10.00
Trade discount 5%
Sales Tax 15%
Net Price
$700 x.05 = $35
$700 - $35 = $665
Sales Tax
$665 x .15 = $99.75
Cost $665.00
Tax
Shipping
Total $774.75
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27. Calculating Actual Sales
Actual sales = Total sales
1 + tax rate
Register receipts total $5,000 for the day, which included a 15% harmonized tax. What are actual sales?
Check:
Sales $4, x .15 = $652.17
$4, $ = $5,000
$5,000 = $4,347.83
1.15
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28. Excise Tax Imposed on luxury items or nonessentials
Tax is based on a percentage of the retail price of a product or service.
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29. Property Tax
Assessed value - The value of property for the purposes of computing property taxes.
Property taxes pay for local fire and police protection, schools, etc . They are based on assessed value.
Assessed value = Assessment rate x Market value
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30. · the selling price for a residential property
In Ontario, a special institution, Ontario Property Assessment Corporation (OPAC), which is responsible for property assessments in this province, uses three different methods for analysis and establishment of property values. These methods are based on three criteria:
·  the selling price for a residential property
·     the generated rental income for office or business property
 ·     the cost of its replacement for an industrial property
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31. · Assessed value x Municipal Tax Rate = Amount of Municipal
According to OPAC property taxes are calculated using an assessed value, a municipal tax rate, and an education tax rate, which is set by the province.
The formula is:
·        Assessed value x Municipal Tax Rate = Amount of Municipal
Property Tax
·        Assessed Value x Education Tax Rate = Amount of Education
·        Municipal Property Tax + Education Property Tax = The Owner’s Property Tax
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32. Calculating Property Tax
The most frequently used formula for calculation of property tax is: product of assessed value of the property and decimal equivalent of the mill rate (Mill is a tenth of 1 cent and 1 thousandth of a dollar):
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33. Expressing Tax Rate Per $100 of Per $1,000 of
By percent assessed value assessed value In mills
7.69% $ $
Per $100 of Per $1,000 of
By percent assessed value assessed value In mills
$40,000 x 7.69% $40,000 = 400 $40,000 = x .001x
$100 $1, $40,000
400 x $ x $76.90
$3, $3, $3, $3,076
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