ok so the amount invested is x
doubled is 2x
compound interst formula is
\(A=P(1+ \frac{r}{n})^{nt}\)
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=?
\(2x=x(1+ \frac{0.12}{4})^{4t}\)
\(2x=x(1+ 0.03)^{4t}\)
divide both sides by x
\(2=(1+ 0.03)^{4t}\)
\(2=(1.03)^{4t}\)
\(2=(1.03)^{4t}\)
take the log₁.₀₃ of both sides
\(log_{1.03}(2)=log_{1.03}(1.03^{4t})\)
we know that \(log_xx^n=n\) so
\(log_{1.03}(2)=4t\)
divide both sides by 4
\(\frac{log_{1.03}(2)}{4} =t\)
use calculator to aprox
5.8624430625
about 5.9 years or 5 years and 10.3 months
