compound interst formula is [tex]A=P(1+ \frac{r}{n})^{nt} [/tex] A=future amount P=present amount r=rate in decimal n=number of times per year it is compounded t=time in years
we know A=2x P=x r=0.12 n=4 t=?
[tex]2x=x(1+ \frac{0.12}{4})^{4t} [/tex] [tex]2x=x(1+ 0.03)^{4t} [/tex] divide both sides by x [tex]2=(1+ 0.03)^{4t} [/tex] [tex]2=(1.03)^{4t} [/tex] [tex]2=(1.03)^{4t} [/tex] take the log₁.₀₃ of both sides [tex]log_{1.03}(2)=log_{1.03}(1.03^{4t})[/tex] we know that [tex]log_xx^n=n[/tex] so [tex]log_{1.03}(2)=4t[/tex] divide both sides by 4 [tex] \frac{log_{1.03}(2)}{4} =t [/tex] use calculator to aprox 5.8624430625 about 5.9 years or 5 years and 10.3 months
