1

I am trying to figure out the best formula for calculating recurring revenue over a period of time. For example:

I charge $10 a month for a subscription services. Every month I get an extra client. What is the simplest formula for calculating this scenario?

For a 12 month period:

10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 + 100 + 110 + 120 = 780

Here is a formula that works but I don't really understand it and am not sure if it is the best way to achieve the desired result.

N * ((N+1) * X/2 )

12*((12+1) * 10/2) = 780

ipengineer
  • 113

1 Answers1

1

Suppose you charge 1 unit per month for each client and at the end each new month you get a new client. Then it should be clear that in $n$ months your revenue will be $$ 1+2+\cdots+n $$ so you're essentially asking for a simple way, not involving $\cdots$, of expressing this sum. Here's a cute solution with an interesting history. Call the sum $S$, so $$ S=1+2+\cdots+n $$ Now write the sum in reverse, so we have $$\begin{align} S&=1+\quad2+\cdots+(n-1)+n\quad\text{and}\\ S&=n+(n-1)+\cdots+2+\quad1 \end{align}$$ Now add these, column-wise. You'll have $n$ terms in the sum, each equalling $n+1$, so $$ 2S=(n+1)+\cdots+(n+1)=n(n+1) $$ and so, dividing by 2, $$ 1+2+\cdots+n=S=\frac{n(n+1)}{2} $$ Now suppose your revenue per transaction was $x$. You'd have that your total revenue in $n$ periods would be $$ \frac{n(n+1)}{2}\cdot x $$ See?

Rick Decker
  • 8,718