I have a problem with transforming a formula for doubling time. It has two variables: increase (i) and number of periods (p).
The original formula: $p = \frac{\log(2)}{\log (1+i)}$.
When I enter $i = 0.05$, it correctly calculates $p = 14.207$.
Now I'm trying to make a formula for "increase". I transformed it to: $i = 10^{\frac{\log(2)}{p}} - 1.$ When I enter $14.207$ periods, it gives me a increase = $0.1189$ (and not $0.05$). Where's my mistake?
The transformations I did:
$p = \frac{\log(2)}{\log (1+i)}$
$\log(1+i) = \frac{\log(2)}{p}$
$1+i = 10^{\frac{\log(2)}{p}}$
$i = 10^{\frac{\log(2)}{p}} - 1$
It gives a wrong answer... Do you see where I made a mistake?
It is using logarithm base $e$. That didn't matter in the first formula, because the difference was cancelled by the two logarithms.
Two solutions: 1) there might be a logarithm spelt 'log10' instead of 'log'
Or, 2) you could use $\exp(\log(2)/p)-1$