To answer this question we will use the following formula for monthly compounded interest:
[tex]I=I_0(1+\frac{r}{12})^{12t},[/tex]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:
[tex]\begin{gathered} I=2000(1+\frac{0.08}{12})^{12\cdot15} \\ \approx2000(1+0.006667)^{180}=2000(1.006667)^{180} \\ \approx2000\cdot3.30692\approx6613.84. \end{gathered}[/tex]Answer: $6613.84.
