Successive Percentage Change

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# Successive Percentage Change - PowerPoint PPT Presentation

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

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### 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

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%

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%

The Formula

(1 ± P1) * (1 ± P2) – 1 = %

where % is written in fractional form (decimal)

P1 = First percentage increase/decrease

P2 = Second percentage increase/decrease

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?
Deriving the Formula (cont.)
• Variables

B = Beginning Value

I = Intermediate Value

F = Final Value

P1 = First Percent Decrease

P2 = Second Percent Decrease

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

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

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