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+(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+(0.06)/(12))^(12t) \\ (8000)/(5000)=1.005^(12t) \\ \ln ((8)/(5))=12\cdot t\ln (1.005)_{} \\ t=(\ln ((8)/(5)))/(12\ln (1.005)) \\ t=7.85 \end{gathered}`

therefore, the answer is 7.9 years