I'm trying to use the following formula to calculate the amount of time it will take an investment at 8% interest to double.
I'm using the following formula:
$Q(t)=Q_0\left(1+\frac{.08}{4}\right)^{4t}$
And to be completely honest, I just can't remember how to correctly apply the rules of exponents, but here was my attempt using an initial investment of $100:
$200 = 100\left(1+\frac{.08}{4}\right)^{4t}$
$\ln2=4t\ln\left(1+\frac{08}{4}\right)$
$\frac{\ln2}{4\ln\left(1+\frac{.08}{4}\right)}=t$
$t=8.75$
Assuming the algebra is correct, did I attempt to solve this correctly?
The calculations of free_mind seems correct to me. I just calculated a version of that exercise in continous time:
$Q_t=2*Q_0=Q_0*e^{r*t}$
$2 = e^{r*t}$
$ln(2)=r*t$
$\frac{ln(2)}{r}=t$
$t=8.66$