Calculating a percent decrease

[Karen]

I am working on a spreadsheet which calcualtes a decrease in base wages,
which is working fine: A1*(1-A2)= X or $15.00 *(1-8%) = $13.80. Howeever,
when I work the formula in reverse, I don't get my original number: $13.80 *
8% = $14.90. Why is that? Thank you.

 

[Fred Smith]

Because that's the way percentages work.

If you invest $100, and lose 25%, you end up with $75. But from there, you
need a 33% return to get your money back.

Or, if the Canadian dollar drops from par to 80 cents, it's dropped 20%. But
to get from there back up to par, it has to increase 25%.

When your base is $15.00, 8% is $1.20. But when your base is $13.80, 8% is
only $1.10.

Regards,
Fred.

 

[joeu2004]

I am working on a spreadsheet which calcualtes a decrease
in base wages, which is working fine: A1*(1-A2)= X or
$15.00 *(1-8%) = $13.80.  Howeever, when I work the formula
in reverse, I don't get my original number: $13.80 *
8% = $14.90. Why is that?

Your algebra is wrong. If A1*(1-A2) = X, then A1 = X / (1-A2), not A1
= X * (1+A2), which is what you really did (that is, you did 13.80*
(1+8%), not 13.80*8%).

For example, 13.80/(1-8%) does indeed equal 15.

Note: Due to anomalies of computer binary arithmetic, it might not
always be __exactly__ equal.