Pre-Algebra 8.6 and 8.7 Applications of Percents

Estimate % of out of % of out of % % Possible answers: Warm Up

Learn to find commission, sales tax, and withholding tax, interest, simple interest, principles, and rates of interest.

commission commission rate sales tax withholding tax interest simple interest principal rate of interest Vocabulary

Real estate agents often work for commission. A commission is a fee paid to a person who makes a sale. It is usually a percent of the selling price. This percent is called the commission rate. Often agents are paid a commission plus a regular salary. The total pay is a percent of the sales they make plus a salary. commission ratesalescommission commission rate  sales = commission

A real-estate agent is paid a monthly salary of $900 plus commission. Last month he sold one condominium for $65,000, earning a 4% commission on the sale. How much was his commission? What was his total pay last month? First find his commission. 4%  $65,000 = ccommission rate  sales = commission Example: Multiplying by Percents to Find Commission Amounts

0.04  65,000 = c Change the percent to a decimal = c Solve for c. He earned a commission of $2600 on the sale. Now find his total pay for last month. $ $900 = $3500 commission + salary = total pay His total pay for last month was $3500. Example Continued

Sales tax is the tax on the sale of an item or service. It is a percent of the purchase price and is collected by the seller.

If the sales tax rate is 6.75%, how much tax would Adrian pay if he bought two CDs at $16.99 each and one DVD for $36.29? CD: 2 at $16.99$33.98 DVD: 1 at $36.29 $36.29 $70.27Total Price  = Convert tax rate to a decimal and multiply by the total price. Adrian would pay $4.74 in sales tax. Example: Multiplying by Percents to Find Sales Tax Amounts

A tax deducted from a person’s earnings as an advance payment of income tax is called withholding tax.

Anna earns $1500 monthly. Of that, $ is withheld for Social Security and Medicare. What percent of Anna’s earnings are withheld for Social Security and Medicare? Think: What percent of $1500 is $114.75? Solve by proportion: n 100 = n  1500 = 100  Find the cross products. Example: Using Proportions to Find the Percent of Tax Withheld

n = % of Anna’s earnings is withheld for Social Security and Medicare. 11, n = 1500n = 11,475Divide both sides by Example Continued

When you borrow money from a bank, you pay interest for the use of the bank’s money. When you deposit money into a savings account, you are paid interest. Simple interest is one type of fee paid for the use of money. I = P  r  t Simple Interest Principal is the amount of money borrowed or invested Rate of interest is the percent charged or earned Time that the money is borrowed or invested (in years)

To buy a car, Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay? First, find the interest she will pay. I = P  r  tUse the formula. I = 15,000  0.09  3 Substitute. Use 0.09 for 9%. I = 4050 Solve for I. Example: Finding Interest and Total Payment on a Loan

Jessica will pay $4050 in interest. P + I = Aprincipal + interest = amount 15, = A Substitute. 19,050 = A Solve for A. You can find the total amount A to be repaid on a loan by adding the principal P to the interest I. Jessica will repay a total of $19,050 on her loan. Example Continued

I = P  r  t Use the formula. I = 1000   18 Substitute. Use for 3.25%. I = 585 Solve for I. Now you can find the total. John’s parents deposited $1000 into a savings account as a college fund when he was born. How much will John have in this account after 18 years at a yearly simple interest rate of 3.25%? Example: Computing Total Savings

P + I = AUse the formula = A 1585 = A John will have $1585 in the account after 18 years. Example Continued

1. The lunch bill was $8, and you want to leave a 15% tip. How much should you tip? 2. The sales tax is 5.75%, and the shirt costs $20. What is the total cost of the shirt? 3. As of 2001, the minimum hourly wage was $5.15. Congress proposed to increase it to $6.15 per hour. To the nearest percent, what is the proposed percent increase in the minimum wage? $21.15 $ % Lesson Quiz: Part 1

4. It costs a business $13.30 to make its product. To satisfy investors, the company needs to make $4 profit per unit. To the nearest percent, what should be the company’s markup? 30% 5. A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in one year? 6. Joshua borrowed $1000 from his friend and paid him back $1050 in six months. What simple annual interest did Joshua pay his friend? 10% $125 Lesson Quiz: Part 2

7. The Jennings borrowed $3000 for home improvements. They repaid the loan and $600 in simple interest four years later. What simple annual interest rate did they pay? 8. Mr. Betts had $120,000 in a retirement account. The account paid 4.25% simple interest. How much money was in the account at the end of 10 years? 5% $171,000 Lesson Quiz: Part 3