Formula for offsetting some additional percentage like an added fee Say I want to pay someone $100.00 but the service I use keeps 3% of the payment I make. Meaning they would only receive $97.00 since they would keep $3. If I increase my payment to $103 they would keep $3.09 meaning they would only receive $99.91. Is there a formula to calculate the exact extra amount I'd need to pay in order to offset the percentage fee?
(I know this is tagged incorrectly but I can't create tags yet and I didn't see any that fit.)
 A: You want to pay x to someone, but services take r%, you have to pay them y.
Since $\large x = y \cdot (1 - \frac r {100})$
Then $\large y = \frac x {1 - \frac r {100}}$
A: If $x$ is the quantity you pay, then they keep $0.97x$. Since you want $0.97x$ to equal $100$, you have
\begin{align*}
0.97 x &= 100\\
x & = & \frac{100}{0.97}\\
x & \approx & 103.0928
\end{align*}
so you would want to give them something between $$103.09$ and $$103.10$ (as it happens, 97% of 103.09 is 99.9973, which would be rounded up to 100 by most, and 97% of 103.10 is 100.007, which would be rounded up to 100.01 by most).
In general, if you want them to get $T$ and they only get $r$% of what you give them, then the formula is that you want to give them $x$, where
$$x = \frac{100T}{r}.$$
A: If you are going to get 97% of x, and you want to get $100, then:
100 = .97x 
(divide each side by .97)
100/.97 = x
A: In general suppose $FV$ is the future value of an asset and $PV$ is the present value of an asset. Then $FV = \frac{PV}{(1-d)^n}$ where $d = i/(i+1)$ (where $i$ is the annual effective interest rate) is the discount rate. In this example, $d = 0.03$, $n=1$ and $FV = 100$. 
