ok so the amount invested is x
doubled is 2x
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
