Section Consumer Mathematics. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Transcription

1 Section 11.1 Consumer Mathematics

2 INB Table of Contents Date Topic Page # June 11, 2014 Test #2 Test 26 June 11, 2014 Test #2 Test Corrections 27 June 11, 2014 Section 11.1 Examples 28 June 11, 2014 Section 11.1 Notes 29 June 11, 2014 Section 11.2 Examples 30 June 11, 2014 Section 11.2 Notes

3 What You Will Learn Percent, Fractions, and Decimal Numbers Percent Change Percent Markup and Markdown Other Percent Problems

4 Percent The word percent comes from the Latin per centum, meaning per hundred. A percent is a ratio of some number to % x x%

5 To Change a Fraction to a Percent 1. Divide the numerator by the denominator to obtain a decimal number. 2. Multiply the decimal number by 100 (which has the effect of moving the decimal point two places to the right). 3. Add a percent sign

6 Example 1: Converting Fractions to Percents Change each of the following fractions to a percent. a) 67 b) c)

7 To Change a Decimal Number to a Percent 1. Multiply the decimal number by Add a percent sign

8 Example 2: Converting Decimal Numbers to Percents Change each of the following decimal numbers to a percent. a) 0.14 b) c)

9 To Change a Percent to a Decimal Number 1. Divide the number by Remove the percent sign

10 Example 3: Converting a Percent to a Decimal Number a) Change 35% to a decimal number. b) Change 69.8% to a decimal number. c) Change 1 2 % to a decimal number

11 Percent Change The percent increase or decrease, or percent change, over a period of time is found by the following formula: Percent change = amount in latest period amount in previous period amount in previous period

12 Percent Change If the amount in the latest period is greater than the amount in the previous period, the answer will be positive and indicate a percent increase. If the amount in the latest period is smaller than the amount in the previous period, the answer will be negative and indicate a percent decrease

13 Example 6: Most Improved Baseball Team In 2010, the Major League Baseball team with the most improved record for winning games was the San Diego Padres. In 2009, the Padres won 75 games. In 2010, the Padres won 90 games. Determine the percent increase in the number of games won by the Padres from 2009 to

14 Percent Markup The following formula represents percent markup or markdown on cost. A positive answer indicates a markup. A negative answer indicates a markdown. Percent markup or markdown on cost selling price dealer's cost = dealer's cost

15 Example 8: Determining Percent Markup Holdren Hardware stores pay $48.76 for glass fireplace screens. They regularly sell them for $ At a sale they sell them for $ Determine a) the percent markup on the regular price. b) the percent markup on the sale price

16 Example 10: Down Payment on a Condominium Home Melissa Bell wishes to buy a condominium home for $189,000. To obtain the mortgage loan, she must pay 20% of the selling price as a down payment. Determine the amount of Melissa s down payment

17 Section 11.2 Personal Loans and Simple Interest

18 What You Will Learn Ordinary Interest The United States Rule Banker s Rule 27

19 Personal Loans The amount of credit extended or the principal of the loan and the interest rate that you may obtain depend on the assurance that you can give the lender that you will be able to repay the loan. Security (or collateral) is anything of value pledged by the borrower that the lender may sell or keep if the borrower does not repay the loan. 28

20 Personal Loans A personal note is a document (or agreement) that states the terms and conditions of the loan. Bankers sometimes grant loans without security, but they require the signature of one or more other persons, called cosigners, who guarantee the loan will be repaid. 29

21 Interest Interest is the money the borrower pays to use the lender s money. Simple interest is based on the entire amount of the loan for the total period of the loan. 30

22 Simple Interest Formula Interest principal rate time i prt p is the principal, amount lent r is the rate of interest, as a decimal t is the time; days, months, or years 31

23 Simple Interest Formula The most common type of simple interest is called ordinary interest. For computing ordinary interest, each month has 30 days and a year has 12 months or 360 days. On the due date of a simple interest note the borrower must repay the principal plus the interest. 32

24 Example 1: Air Conditioning Loan Sherry Tornwall needs to borrow $6200 to replace the air conditioner in her home. From her credit union, Sherry obtains a 30-month loan with an annual simple interest rate of 5.75%. a) Calculate the simple interest she is charged on the loan. 33

25 Example 1: Air Conditioning Loan b) Determine the amount, principal plus interest, Sherry will pay the credit union at the end of the 30 months to pay off her loan. 35

26 Discount Notes In another type of loan, the discount note, the interest is paid at the time the borrower receives the loan. The interest charged in advance is called the bank discount. 38

27 Example 4: True Interest Rate of a Discount Note Siegrid Cook took out a $500 loan using a 10% discount note for a period of 3 months. Determine a) the interest she must pay to the bank on the date she receives the loan. b) the net amount of money she receives from the bank. c) the actual rate of interest for the loan. 39

28 The United States Rule A payment that is less than the full amount owed and made prior to the due date is known as a partial payment. A Supreme Court decision specified the method by which these payments are credited. The procedure is called the United States rule. 42

29 The United States Rule The United States rule states that if a partial payment is made on the loan, interest is computed on the principal from the first day of the loan until the date of the partial payment. The partial payment is used to pay the interest first; the rest of the payment is used to reduce the principal. The balance due on the date of maturity is found by computing interest due since the last partial payment and adding this interest to the unpaid principal. 43

30 Banker s Rule The banker s rule is used to calculate simple interest when applying the United States rule. The banker s rule considers a year to have 360 days, and any fractional part of a year is the exact number of days of the loan. 44

31 Table

32 Table

33 Example 8: Using the United States Rule Cathy Panik is a mathematics teacher, and she plans to attend a national conference. To pay for her airfare, on November 1, 2010, Cathy takes out a 120-day loan for $400 at an interest rate of 12.5%. Cathy uses some birthday gift money to make a partial payment of $150 on January 5, a) Determine the due date of the loan. b) Determine the interest and the amount credited to the principal on January 5. c) Determine the interest and the amount credited to the principal on February 2. d) Determine the amount that Cathy must pay on the due date. 47

34 Example 8: Using the United States Rule Cathy Panik is a mathematics teacher, and she plans to attend a national conference. To pay for her airfare, on November 1, 2010, Cathy takes out a 120-day loan for $400 at an interest rate of 12.5%. Cathy uses some birthday gift money to make a partial payment of $150 on January 5, a) Determine the due date of the loan. 48

35 Example 8: Using the United States Rule Cathy Panik is a mathematics teacher, and she plans to attend a national conference. To pay for her airfare, on November 1, 2010, Cathy takes out a 120-day loan for $400 at an interest rate of 12.5%. Cathy uses some birthday gift money to make a partial payment of $150 on January 5, b) Determine the interest and the amount credited to the principal on January 5. 49

36 Example 8: Using the United States Rule Cathy Panik is a mathematics teacher, and she plans to attend a national conference. To pay for her airfare, on November 1, 2010, Cathy takes out a 120-day loan for $400 at an interest rate of 12.5%. Cathy uses some birthday gift money to make a partial payment of $150 on January 5, c) Determine the interest and the amount credited to the principal on February 2. 50

37 Example 8: Using the United States Rule Cathy Panik is a mathematics teacher, and she plans to attend a national conference. To pay for her airfare, on November 1, 2010, Cathy takes out a 120-day loan for $400 at an interest rate of 12.5%. Cathy uses some birthday gift money to make a partial payment of $150 on January 5, d) Determine the amount that Cathy must pay on the due date. 51