Percent, Sales Tax and Income Tax

• Percentage is a unitless measurement of parts per hundred.
  • Given a population
  • and a number of occurences of something
  • The percentage is (occurences)/population
  • It is normally a number between 0 and 1
  • When writing as a percent, multiply this by 100 and add %
• Example 1: express 1/5 as a percentage

  1/5 = .2   
  .2 x 100 = 20%
     

• Changing between decimals and percentage
  • Percentage to decimal : divide by 100
  • Decimal to percentag : multiply by 100
• Example 2

  A. express .345 as a percentage    .345x100% = 34.5%
  B. Express 28.7% as a decimal   .287
     

• A = P·B
• A is P percent of B
  • Example 1: The sales tax rate is 6%. What is the sales tax on $4.37?

    tax is 6% of price
    T = .06*$4.37 = $.26
    What is the total cost?
         $4.37 + $.26 = $4.63
           

  • A shirt costing $43.52 is 35% off. What is the final price?

    First we compute the discount
    discount is 35% of 43.52
    d= .35x$43.52 = $15.23
    Price = Original Price - discount
    P = 43.52 - 15.23 = 28.29
           

• Percentage increase and decrease
  • (new amount - old amount)/old amount
  • Problem 66 page 454

    Old Price = 380
    New Price 266
    
    Percentage Change = (266-380)/380  = -30% 
           

• Income Tax
  • Compute gross income
    • Add up all sources of income that qualify
    • Salary
    • Investments (most of them)
    • Other forms of income
  • Compute adjusted income
    • Subtract what you are allowed to subtract
    • Medical expenses (some)
    • Interest on primary residence
    • Charitable contributions.
    • Other Strange Stuff.
    • There is a standard deduction, which you can take in place of computing this.
    • This is money the government pretends you never earned.
  • Compute tax.
    • Graduated income tax.
    • Pay 10% of first bit of income.
    • 15% on next bit.
  • Compute adjustments
    • Some things count as tax credit, and these are subtracted from the amount of taxes you owe.

Homework