Question

You deposit $2000 in an account earning 8% interest compounded monthly. How much will you have in the account in 15 years?

Answer 1

To answer this question we will use the following formula for monthly compounded interest:

`I=I_0(1+(r)/(12))^(12t),`

where I₀ is the initial amount, r is the interest rate as a decimal number, and t is the number of years.

Substituting I₀=2000, r=0.08, and t=15 we get:

`\begin{gathered} I=2000(1+(0.08)/(12))^(12\cdot15) \\ \approx2000(1+0.006667)^(180)=2000(1.006667)^(180) \\ \approx2000\cdot3.30692\approx6613.84. \end{gathered}`

Answer: $6613.84.