The formula for compound interest is written as [tex]A = P(1 + \frac{r}{n})^{nt}[/tex], where P is the principal (initial amount), r is the rate of interest, n is the number of times it's compounded per year, and t is the time in years. With the values from this problem plugged in, it looks like:
[tex]A = 4000(1.05})^{t}[/tex]
Since you're trying to find when your money will double, put 8000 for A and solve for t :
[tex]8000 = 4000(1.05})^{t} \\ \\ 2 = (1.05})^{t} \\ \\ t=log_{1.05}2 \\ \\ t = 14.20669908289 [/tex]
It will take approximately 14.21 years, or about 14 years, 2 months, and 16 days, for the money to double.
