1. Successive percents

2. Imagine that your boss raised your salary last year by 10%. Now, because of tough economic times, he is going to cut it by 10%. What will be your new salary, relative to where you started?

3. NOT THE SAME! LESS!

4. Why? The raise was computed as 10% of the original salary. The reduction -- computed as 10% of the original salary plus the 10% raise – is more than the raise.

5. Test it out in Excel

6. General point: Cannot add or subtract successive percents. Because they have different bases they are not additive.

7. Successive percents formula In the following slides, X equals the original quantity of something. Percentage change/difference is treated in decimal form (percentage; p/100) The phrase 1+p 1 means “1plus or minus p 1 ” depending on the sign of p 1

8. Method for solving successive percent problems: computing values

9. Time Period Pct. Change End Value 1p1p1 X+(X*p 1 ) or X*(1+p 1 )

10. In other words, start by converting “percent difference/change” to “percentage of”

11. Time Period Pct. Change End Value 1p1p1 X*(1+p 1 ) 2p2p2 X*(1+p 1 )*(1+p 2 )

12. Time Period Pct. Change End Value 1p1p1 X*(1+p 1 ) 2p2p2 X*(1+p 1 )*(1+ p 2 ) 3p3p3 X*(1+p 1 )*(1+ p 2 )*(1+ p 3 )

13. The process on can be extended without limit

14. To compute cumulative percentage change/difference, convert “percentage of” result back to percentage change/difference.

15. Formula for computing cumulative percentage change: (1+p 1 ) (1+p 2 )-1