Modelling a decreasing growth rate - I want to calculate a growth model in discrete time such that my client base grows from 5 to 10000 in 8 years?

Asked Sep 12 '22 at 21:19

Active Sep 13 '22 at 07:53

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I am looking at a financial model such that at time=0 the number of clients I have is 5. If I consider discrete time such that the number of clients at time t is equal to:

y(t) = y₀ * ∏ ^t-1₀ (1 + r(i))

I want to know if each period is a month and in 8 years I have 10000 clients (so 96 months total discrete periods) where the growth rate r(i) decreases each month over the 8 years; what formula for r(i) can I use to achieve this or what formula can be used to help me calculate this please based on a changing inital growth rate?

edited Sep 13 '22 at 07:53

asked Sep 12 '22 at 21:19

james birley

it is not 0^(t-1) it is the multiplicative sum of 1+r(i) for i from 0 to t-1. I will adjust to make this clearer – james birley Sep 13 '22 at 07:53
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This question is probably better suited for the [Mathematics](https://math.stackexchange.com/) Stack Exchange. – Hymns For Disco Sep 13 '22 at 09:33

Modelling a decreasing growth rate - I want to calculate a growth model in discrete time such that my client base grows from 5 to 10000 in 8 years?

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