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.)

-

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 $$x = \frac{100T}{r}.$$

-
Oh duh. I didn't think of it like that. – Spencer Ruport Mar 1 '11 at 20:47

You want to pay x to someone, but services take r%, you have to pay them y.

Since

x = y * (1 - (r/100))


Then

y = x * / (1 - (r/100))

-

If you are going to get 97% of x, and you want to get $100, then: 100 = .97x (divide each side by .97) 100/.97 = x - In general suppose$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\$.

-