I can't reproduce the intermediate steps when it comes to solving $n$ in:
$$333.443,35 = 30.000\frac{1,02^n - 1}{1,02^n \cdot 0,02}$$
It says
$$n = - \frac{\log (1-\frac{333.443,35}{30.000}) \cdot 0.02}{\log(1,02)}$$ $$= 12,7$$
Looks like $333.443,35$ was divided by $30.000$ first. Then somehow $\log$ was applied and nominator became denominator.
Can someone show me step-by-step what happened?
This is of the form $M=s \frac{r^n-1}{r^n(r-1)}$, where everything except $n$ is known.
$$\frac Ms = \frac{r^n-1}{r^n(r-1)} \Rightarrow (r-1) \frac Ms=1-\frac {1}{r^n} \\ \Rightarrow r^{-n}=1-(r-1) \frac Ms$$
Now take logs on both sides and divide by $\ln r$ It looks to me like $0.02$ should be inside the parentheses.