Needing to meet a certain amount of funding, minus my fee

[jberrym151]

Hello,
I work in an industry were I help secure people funding for business startups. We do this for free, until they start to receive funds. We invoice a fee, anywhere between 10-15%. Its pretty easy to figure out how much they owe us. What I have found difficult is nailing down the exact amount of funding they would need to receive, to cover my fee, as well as hit a number they need. For instance, 15% of $100,000 is $15,000, leaving them with $85,000. Let's say they need to walk away with $100,000 after my fee. Is there a formula to determine the gross amount needed, minus my fee (which changes from 8-15%) to net a client a certain amount of funds?

 

[blamocur]

If you fee rate is [imath]r[/imath] (0.1 -- 0.15), and the total amount of funds is [imath]f[/imath] then you get [imath]rf[/imath] and the startup gets [imath](1-r)f[/imath]. If they actually need the amount [imath]d[/imath] then the [imath]d = (1-r)f \Rightarrow f = \frac{d}{1-r}[/imath]. Thus if they need $100k and you charge them 15%, then they need to ask for [imath]f = \frac{100000}{1-0.15} \approx \$117647[/imath], of which your fee will be $17647.