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Successive Percentage Change - PowerPoint PPT Presentation


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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

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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
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
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
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
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 cont7
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 formula8
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 cont9
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