1 / 9

Successive Percentage Change

Successive Percentage Change. Jeans are on sale for 40% off the retail price. The retail price is $40.00. If you have a coupon, you can receive an additional 20% off the sale price. What is the overall percentage savings?. Determine the sale price: $40 – ($40 * .40) = $24

nate
Download Presentation

Successive Percentage Change

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Successive Percentage Change

  2. Jeans are on sale for 40% off the retail price. The retail price is $40.00. If you have a coupon, you can receive an additional 20% off the sale price. What is the overall percentage savings? Determine the sale price: $40 – ($40 * .40) = $24 Determine the final price with coupon: $24 – ($24 * .20) = $19.20 Determine the overall percentage change: new – old = $19.20 - $40 = - 0.52 old $40 -0.52 * 100% = Savings of 52%

  3. VISUALLY Determine the sale price: $40 – ($40 * .40) = $24 Determine the final price with coupon: $24 – ($24 * .20) = $19.20 Determine the overall percentage change: new – old = $19.20 - $40 = - 0.52 old $40 -0.52 * 100% = Savings of 52%

  4. The Formula (1 ± P1) * (1 ± P2) – 1 = % where % is written in fractional form (decimal) P1 = First percentage increase/decrease P2 = Second percentage increase/decrease

  5. Deriving the Formula • The overall percentage change does NOT depend on the Beginning Value (B). Can we show this by determining a process (formula) that includes just the two percents?

  6. Deriving the Formula (cont.) • Variables B = Beginning Value I = Intermediate Value F = Final Value P1 = First Percent Decrease P2 = Second Percent Decrease

  7. Deriving the Formula (cont.) First find the intermediate price B – (B * P1) = I Then find the final price I – (I * P2) = F Then find the overall percentage change F - B B

  8. Deriving the Formula We can rewrite the first equation: B – (B * P1) = I As B * ( 1 – P1) = I We can rewrite the second equation: I – (I * P2) = F As I * (1 – P2) = F

  9. Deriving the Formula (cont.) Substitute these into final equation: F – B B So , since we found that F = I*(1-P2) I*(1-P2) – B B And we also know that I = B*(1-P1) B*(1-P1) * (1-P2) – B B The B’s cancel out to arrive at: (1-P1) * (1-P2) - 1

More Related