calculating a percentage

J

Jennnifer

If I receive a 7% rebate on my total cost of $100,00 why do the 2 formuals
produce differnet results?

=100,000*.93 = $93000

=100,000/1.07 = $93,457

Which is the correct formula to use?
 
D

David Biddulph

The difference is because (1-x) is not the same as 1/(1+x) [though they get
closer to each other as x tends towards zero]

To take a more extreme example, a 100% reduction takes the value down to
zero, but to divide by (1+100%) will merely halve the value.
Another way of looking at it is that if you have a 50% reduction it will
then need a 100% increase to get back to the original value.

A 7% rebate would be the multiplication by 93%, not division by (1+7%).
 
G

Gary''s Student

The first formula gives you the actual cost after the discount has be removed.
 
D

Don

think of it this way mathamaticly,
100,000/1.07 = 100000 * x
devide 100,000 on both sides then x = 1/1.07 = 0.934579 something. The
first one is correct but the 2nd one will look like a 7% rebate but will
benifit the seller more than the buyer
 
T

Tyro

I assume you mean $100,000. A 7% rebate of $100,000 is $100,000 * 7% =
$7,000. So, $100,000 - $7,000 = $93,000 which is your final cost, not your
rebate. Also 100,000/1.07 is the same as 100,000 * 1/1.07 = 100,000 *
0.9345794392523364485981308411215, clearly not equal to 100,000 * .93. If
you receive $7,000 as a rebate at 7% you may compute the original cost by
dividing the rebate, 7,000 by 7% which gives: 100,000.

Tyro
 
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