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Successive Percents!!

This content delves into calculation methods for successive percentage changes using practical examples involving discounts on jeans and tax cuts. It explains how to determine the overall percentage savings from multiple discounts, showcasing step-by-step calculations for clarity. Additionally, it evaluates a politician's promise of tax cuts, exploring the actual percentage change over three years. The content also analyzes price changes in crude oil to reflect real-world volatility. Learn how to apply these formulas effectively in various scenarios.

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Successive Percents!!

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  1. Successive Percents!!

  2. Question. 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?

  3. Jeans The sale price: $40 - $40*.40 = $40 - $16 = $24 Determine the final price with coupon: $24 - $24*.20 = =$24 – $4.80 = $19.20

  4. Jeans The overall percentage change?? C’mon…

  5. The Formula (1 ± P1) *(1 ± P2) – 1 = % (where the % is written as a decimal) (1-.4)*(1-.2) – 1 = -.52

  6. A politician promises, “If elected, I will cut your taxes by 20% for each of the first three years of my term, for a total of 60%.” Evaluate the promise.

  7. Let’s say we start with 3%. If he/she cuts them by 20% in the first year we’ll be at: • Tax rate after 1st year = .03 - (.03*.2) = .024 • Tax rate after 2nd year = .024 – (.024*.2) = .0192 3. Tax rate after 3rd year = .0192 – (.0192*.2) = .01536

  8. Was the actual percent change 60%?

  9. Spot prices for crude oil are rather volatile.  From 1998 to 1999, spot prices for crude oil decreased by 28%.  From 1999 to 2000, they increased by 106%.  What was the percentage change over the two year period from 1998 to 2000?

  10. One Way: (1 ± P1) *(1 ± P2) – 1 = % (1 - .28)*(1 + 1.06) - 1 = 0.4832 = 48.32%

  11. Second Way: Let’s say start with $100 for a barrel in the beginning of 1998. Beginning of 1999… $100 – ($100*.28) = $72 Beginning of 2000 … $72 + ($72*1.06) = $148.32 = 48.32%

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