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MTH 150
SURVEY OF MATHEMATICS
Chapter 11
CONSUMER MATHEMATICS
11.1 Percent
11.2 Personal Loans and Simple Interest
11.3 Personal Loans and Compound Interest
11.4 Installment Buying
11.5 Buying a House with a Mortgage
Brigitte Martineau Chapter 11 - Consumer Mathematics
11.1 – Percent
What is a Percent or Percentage?
Convert a decimal into a percentage
- Multiply the decimal number by ________
- Add a percent sign
Examples:
- Convert 0.49 to a percentage
- Convert 0.651 to a percentage
Convert a percent into a decimal
- Divide the number by _________
- Remove the percent sign
Examples:
- Convert 37% into a decimal
- Convert 65.3% in to a decimal
Convert a fraction into a percent
- Divide the ______________________ by the _________________________ using a calculator.
- Multiply the quotient by 100 (which has the effect of moving the decimal point ______ places to the ___________
- Add a percent sign
Brigitte Martineau Chapter 11 - Consumer Mathematics
The number of people audited by the IRS fell from 1942 in 1996 to 618 in 2000. What is the percentage decrease from 1996 to 2000?
The graph shows the rise of the minimum hourly wage from 1938 to 1997
Determine the percent increase from 1938 to 1997
Problems of type N% of a = b
- To find a percentage of a total, multiply the percent (in decimal form) by the total.
Find 50% of 8 apples
- To determine a percent, divide the number by the total
I’m taking 30 of the 90 computers. What percent is that?
Brigitte Martineau Chapter 11 - Consumer Mathematics
EXAMPLES:
- Find 30% of 20 toys
- Find 80% of 30 students
- Find 10% of 60 computers
- Of the 15 people invited to my party, 12 came. What percent is that?
- Only 17 of my 30 students passed. What percent is that?
- 3% of what number is 15?
- 5% of what number is 13?
- 80% of what number is 320?
Brigitte Martineau Chapter 11 - Consumer Mathematics
11.2 – Personal Loans and Simple Interest
Some background terminology:
Principal of the loan
Credit
Security
Interest
Simple Interest
Rate
The simple interest formula
Interest = Principal * Rate* time I = PRT
Notes: Always assume 30 days per month, 12 months and 360 days per year.
Examples :
- If we borrowed $2000 for 2 years at a rate of 4.5% how much interest would we pay?
Brigitte Martineau Chapter 11 - Consumer Mathematics
- If we borrowed $2000 for 9 months at a rate of 4.5% how much interest would we pay?
- If we borrowed $2000 for 30 days at a rate of 4.5% how much interest would we pay?
- Find the missing quantity
Principal Rate Time Interest Amount repaid
a. $ 1,200 8% / year 6 months
b. $6,000 2 years $1,
c. 4 years $2,000 $12,
d. $7,000 10% / year $8,
Brigitte Martineau Chapter 11 - Consumer Mathematics
Examples:
- Find the exact time from May 3 to November 15.
- Find the exact time from January 4 to April 8 when the loan is due in a leap year
- Find the exact time from October 8 to December 3 when the loan is due in a leap year.
- Find the due date of the loan, using the exact time, if the loan is made on April 14 for 100 days.
- Find the due date of the loan, using exact time, if the loan is made on July 27 for 230 days.
What is a Partial Payment?
The United States Rule for Making Partial Payments
- A Supreme Court decision specified the method by which partial payments are credited and it’s called the United States rule.
- The partial payment first pays off the interest for the time that’s gone by (find this using I = prt), and then the rest of the partial payment is applied to the principal.
- 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. The Banker’s rule is used to calculate the simple interest when applying the United States rule.
Brigitte Martineau Chapter 11 - Consumer Mathematics
Examples:
- Joe borrows $4000 on a note dated March 14 with simple interest of 5% for 90 days. He made a partial payment of $500 on April 1. How much will he owe on the date of maturity?
- The Cookie Company signed a $2000 note dated August 5th^ with simple interest of 7% for 110 days. The company made a partial payment of $300 on September 10. Find the amount due on the maturity date of the loan.
Brigitte Martineau Chapter 11 - Consumer Mathematics
11.3 – Personal Loans and Compound Interest
What is compound interest?
Comparison of simple interest versus compound interest: $1000 loan for 4 years at 10% a year
First, let’s look at the way interest rate are expressed.
- Compounded annually means how many times a year?
- Compounded semiannually means…………
- Compounded quarterly means
- Compounded monthly means
- Compounded biweekly means
- Compounded twice a month
Brigitte Martineau Chapter 11 - Consumer Mathematics
Compound Interest formula
The final amount (A) includes principal and interest.
Examples
- $2000 for 5 years at 2% compounded semiannually. Use the formula to compute a. The total amount b. The interest earned
- $2000 for 5 years at 2% compounded monthly.. Use the formula to compute a) The total amount b) The interest earned
- $2000 for 5 years at 2% compounded daily. a) The total amount b) The interest earned
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