Answer:
170.202 years
Step-by-step explanation:
From the compound interest formula, that has interest rate in times per year but compounds monthly we have
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A is the amount you want to save, P is the principal (what you put down, in this case 100), r is the anual interest rate, n is 12 i.e the times it compounds, and t is the amount of years it will take. So we have data for all variables but t.
Solving for t we have
[tex]\frac{A}{P}=(1+\frac{r}{n})^{nt}[/tex]
taking logs
[tex]log(\frac{A}{P})=nt \,log(1+\frac{r}{n})[/tex]
finally
[tex]t = \frac {log(\frac{A}{P}) }{ n[log(1 + \frac{r}{n})]}[/tex]
replacing and calculating we get t=170.202
