Successive percents. 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.

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Presentation transcript:

Successive percents

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?

NOT THE SAME! LESS!

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.

Test it out in Excel

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

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

Method for solving successive percent problems: computing values

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

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

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

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 )

The process on can be extended without limit

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

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