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…

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

7. 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.

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

9. Was the actual percent change 60%?

10. 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?

11. One Way: (1 ± P 1 ) *(1 ± P 2 ) – 1 = % (1 -.28)*(1 + 1.06) - 1 = 0.4832 = 48.32%

12. 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%