FORMULABANK

When one wants to find the number of periods and the initial value, the final value, and the percentage growth per period are known.

$n=\frac{\ln \left(\frac{K_n}{K_0}\right)}{\ln (1+r)}$

K_n = The final capital/the final value
K₀ = The initial capital/the initial value
r = The interest rate/growth rate in % per period
n = Number of periods