ok, da equation yo want is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A=future amount P=amount deposted or amount now r=rate in decimal form n=number of times a year compounded t=time in years
so given r=9%=0.09 n=2 t=t
and P and A are unknown wait, we want ending to be triple begining so A=3P
so [tex]3P=P(1+\frac{0.09}{2})^{2t}[/tex] [tex]3P=P(1+0.045)^{2t}[/tex] [tex]3P=P(1.045)^{2t}[/tex] divide both sides by P [tex]3=(1.045)^{2t}[/tex] take ln of both sides [tex]ln(3)=ln((1.045)^{2t})[/tex] [tex]ln(3)=2t(ln(1.045))[/tex] divide both sides by 2ln(1.045) [tex]\frac{ln(3)}{2ln(1.045)}=t[/tex] use calculator 12.4794≈t
