For annual (n=1) and monthly (n=12) use the following:
\((1+ \frac{r}{n})^{25n} = 2\)
Where r is rate per period in which 1 will grow to 2 in 25 years.
To solve for r, take reciprocal of exponent and apply to both sides.
\(1+ \frac{r}{n} = 2^{\frac{1}{25n}} \\ \\ r = n(2^{\frac{1}{25n}} - 1)\)
Now just sub in value for n to get growth rates.
For continuous growth use the following:
\(e^{25r} = 2\)
Solve using natural log.
\(ln(e^{25r}) = ln(2) \\ \\ 25r = ln(2) \\ \\ r = \frac{ln(2)}{25}\)
