Asum of money is invested at 12% compounded quarterly. about how long will it take for the amount of money to double?

Ok so the amount invested is x
doubled is 2x

compound interst formula is

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=?



divide both sides by x



take the log₁.₀₃ of both sides

we know that so

divide both sides by 4

use calculator to aprox
5.8624430625
about 5.9 years or 5 years and 10.3 months

Do you need with the x value for the minimum? its always between the two intercepts for a parabola