Calculating monthly compounded interest

Question

To solve the problem

How long does it take for an investment to double in value if it is invested at 8% compounded monthly?

I figured like this: $$2P = P(1 + 0.08)^t$$ where $P$ is an arbitrary principle investment and $t$ is the time in months. I then solved with logs, $$\log_{1.08}2 = t \approx 9.006$$ However, the back of the book gives $t \approx 104.28$. Where is my mistake?

Answer 1

You have set up the wrong formula for monthly compounded interest. It should be

$$ 2P = P\left(1 + \frac{0.08}{12}\right)^{t} $$

where $t$ is in months.

Note that the answer you have is for $t$ in years, which is about 108 months, so its not as wrong as it might first look (it's still incorrect though).

Answer 2

The book's answer makes sense if the interest is not 8% per month, but 8% "per annum", or more precisely $\frac8{12}$% per month.

(I'm getting 104.32 rather than 104.28 under that assumption, but that may just be a rounding issue).