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When a quantity is increasing in time by the same fraction every period, it is said to exhibit compound growth - every time period it increases by a larger amount.
It is possible to show that the behaviour of the quantity over time follows the law
x(t) = x(0) * exp(r * t)
x(t)is the value of the quantity now
x(0)is the value of the quantity at time t = 0
tis time in units of [time_period]
ris the growth rate in units of 1 / [time_period]
From the equation above, to calculate a growth rate you need to know:
- The value at the start of a period
- The value at the end of a period
- The duration of the period
Then, following some algebra, the growth rate is given by
r = ln(x(t) / x(0)) / t
For a concrete example, assume a table with columns:
num_this_month- this is
num_last_month- this is
t(in years) =
datetime_diff(this_month, last_month, month) / 12
In the following then,
growth_rate is the equivalent yearly growth rate for that month:
To better depict the effects of a given growth rate, it can be converted to a year-on-year growth factor by inserting into the exponential formula above with t = 1 (one year duration).
yoy_growth = x(1) / x(0) = exp(r)
It is always sensible to spot-check what a growth rate actually represents to decide whether or not it is a useful metric.