Reversing a percentage increase

[Roger]

I was calculating the total price of a home I could afford based on a
mortgage payment and then I got curious what the value would be if I added a
6% down payment into the mix so that it would return me to my original price.

For example:
If the value is $250,000 and I increase it by 6% the value goes up to
$265,000. But if I subtract 6% from $265,000 I end up with $249,100. How can
I properly calculate the increase so that it will return me to my original
amount of $250,000?

 

[Graham H]

Hi Roger,
If your 265,000 is in cell C1 and your 6 is in cell B1 the the original value
is returned by C1/(1+B1%)

HTH
Graham

 

[Bernard Liengme]

Graham has told you HOW.
Here is the WHY.
You increased 250k by 6% to get 265k
To revert, you must decrease 265k by the SAME amount, that is by 6% of 250k
(not 6% of 265k)
best wishes

 

[Roger]

Thank you. What you and Graham wrote works and makes sense, but I'm actually
trying to get the inverse result. So let me pose the question a different
way. How can I increase $250,000 so that the result is $265,957.50 which
would allow me to subtract 6% and return to $250,000. (Or something that is
fairly close even if it's not accurate to the decimal.) Or stated
differently, how could I determine that I actually wanted to add 6.383%
percent to $250,000 to get the answer I was looking for.

I figured it out by trial and error, and not so much with an equation that
would allow me to plug in ANY percentage to get similar results.

 

[Roger]

Yeah. That works.

Well, seeing that the way you want to get from 265,957.50 or therabouts to
250,000 is to multiply by (1-6%), did you think that the way to get from
250,000 to 265,957.50 or thereabouts is to *divide* by (1-6%) ?