This comes down to all those algebra classes no one thought they’d ever need in real life. I can’t teach algebra here, but the basics:

X = base year (from which all other years follow, i.e., your B6 amount)

Let B = your discount. Rather than thinking of it as what is taken away, however, we should think of B as what *remains*. This leaves us with XB (which, in your example case, is X times .92 or 92%). In effect then this is 1-*your B9 amount*.

Let A = your retention rate.

We then arrive at XA-XB, which we can rewrite as X(A-B).

X is a constant now, and the A-B portion will apply every year for each of Z years, i.e., for four years: X(A-B)z1 + X(A-B)z2 + X(A-B)z3 + X(A-B)z4 (where Z1, Z2, etc. are an exponent for each year).

In Google Sheets, your B13 formula would then look like this:

`=ArrayFormula(SUM(ROUND(B6*(B8*(1-B9))^(B11-SEQUENCE(B11,1)),2)))`

The `SEQUENCE`

will form the exponents (^) for as many years as requested, and `SUM`

will sum that list.

`ROUND( ... ,2)`

will round each of the exponential years to two decimal places (i.e., standard dollars-and-cents).