I wonder if you can help me?
I have found similar answers to this question but they don't seem to work.
I am after a formula or an excel formula so I can add a percentage to a number, then when I discount the same percentage off the larger figure I get back to exactly the same figure.
The reason for this is because I sell products at a price, some of my customers have special terms when they purchase so I add a percentage onto the selling price to cover these terms. Then when this percentage is discounted off the inflated cost, I need the selling total to go back to the original selling price.
For instance:
If I sell at £1.00,
Customer A has terms of 10%, so I need to add 10% onto 1.00, which is £1.10.
Then when I take 10% off £1.10, which is £0.11p, this returns to £0.99p, which is lower than my original selling price.
If anyone could help with a formula to explain the answer it would be amazing!
I would need the formula to work with different selling prices and different percentages.
Thanks in advance!
Adam
Best Answer
If you take $99\%$ off $€100$, you get $€1$. Then if you add $99\%$ to $€1$, you get $€1.99$, much less than $€100$ because you didn't consider $99\%$ of the same thing.
In general adding $x\%$ is multiplying by $1+\frac x{100}$, so if you want the reverse of that you need to divide by $1+\frac x{100}$, which is the same as multiplying by $\frac{1}{1+\frac x{100}}$. Now
$$\frac{1}{1+\frac x{100}}=1-\frac{x}{100+x}$$ so the reverse of adding $x\%$ is subtracting $(100\cdot \frac{x}{100+x})\%$
Example: $x=10$; the reverse operation of $+10\%$ is $-(100\cdot \frac{10}{100+10})\%\simeq -9.09\%$