Question

$ 2000 principal earning 5% compounded annually after 3 years. Find the balance in the account using exponential function model.

Answer 1

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:

`\begin{gathered} FV(n)=PV\cdot(1+r)^n \\ FV(n)=2000\cdot1.05^n \end{gathered}`

Then, for n=3, we will have:

`\begin{gathered} FV(3)=2000\cdot1.05^3 \\ FV(3)=2000\cdot1.157625 \\ FV(3)=2315.25 \end{gathered}`

Answer: the balance after 3 years is $2315.25.