We have a principal of $2000 (PV=2000) that is invested at an annual rate of 5% (r=0.05) compounded anually.
We have to find the value (FV) after 3 years (n=3).
We can write this as an exponential model as:
[tex]\begin{gathered} FV(n)=PV\cdot(1+r)^n \\ FV(n)=2000\cdot1.05^n \end{gathered}[/tex]Then, for n=3, we will have:
[tex]\begin{gathered} FV(3)=2000\cdot1.05^3 \\ FV(3)=2000\cdot1.157625 \\ FV(3)=2315.25 \end{gathered}[/tex]Answer: the balance after 3 years is $2315.25.
