Question

If Guillermo deposits $5000 into an account paying 6% annual interest compounded monthly, how long until there is $8000 in the account?

Answer 1

We have the following:

The formula in this case is the following:

$A=P(1+\frac{r}{n})^{nt}$

solving for t:

replacing

A is 8000, P is 5000, n is 12 and r is 6% (0.06)

$\begin{gathered} 8000=5000(1+\frac{0.06}{12})^{12t} \\ \frac{8000}{5000}=1.005^{12t} \\ \ln (\frac{8}{5})=12\cdot t\ln (1.005)_{} \\ t=\frac{\ln (\frac{8}{5})}{12\ln (1.005)} \\ t=7.85 \end{gathered}$

therefore, the answer is 7.9 years