Question

Suppose Deon places $4000 in an account that pays 12% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.

Answer 1

The formula for compounded interest is

$A=P(1+r)^t$

We have

P = 4000

r = 12% = 0.12

t = time in years

Therefore

$\begin{gathered} A=4000(1+0.12)^t \\ \\ A=4000\cdot(1.12)^t \end{gathered}$

a)

Now let's evaluate that function at t = 1

$\begin{gathered} A=4000\cdot(1.12)^t \\ \\ A=4000(1.12)^1 \\ \\ A=4000\cdot1.12 \\ \\ A=4480 \end{gathered}$

Therefore at the end of 1 year, he would have $4480

b)

Now let's do it for t = 2, we have

$\begin{gathered} A=4000\cdot(1.12)^t \\ \\ A=4000\cdot(1.12)^2 \\ \\ A=4000\cdot1.2544 \\ \\ A=5017.6 \end{gathered}$

At the end of 2 years, he would have $5017.6