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google sheets – Calculating a total value based on X periods, that takes the previous period into account, without intermediate calculations?

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).

Posted on January 14, 2021Author Proxies123Tags account, based, calculating, calculations, Google, intermediate, period, Periods, previous, Sheets, takes, total

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