Calculating the time for 8% to double an investment when compounded quarterly

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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?

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The calculations of free_mind seems correct to me. I just calculated a version of that exercise in continous time:

$Q_t=2*Q_0=Q_0*e^{r*t}$

$2 = e^{r*t}$

$ln(2)=r*t$

$\frac{ln(2)}{r}=t$

$t=8.66$