Question

Suppose Chang places $4000 in an account that pays 16% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.

Answer 1

Given:

The current amount is $4000.

The interest rate is 16%.

Explanation:

(a):

There are also given that the time for 1 year.

Now,

To find the total amount after the end of 1 year, we need to use the compound interest formula:

So,

From the formula:

$A=P(1+\frac{r}{n})^{nt}$

Where,

$\begin{gathered} P=4000 \\ r=16\%=0.16 \\ n=1 \\ t=1 \end{gathered}$

Then,

Put the values into the above formula:

So,

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=4000(1+\frac{0.16}{1})^{(1)} \\ A=4000(1.16) \\ A=4640 \end{gathered}$

(b):

For 2 years:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=4000(1+\frac{0.16}{1})^2 \\ A=4000(1.16)^2 \\ A=4000(1.35) \\ A=5400 \end{gathered}$

Final answer:

Hence, the final amount after the end of 1 year and 2 years is shown below:

$\begin{gathered} (a):A=4640 \\ (b):A=5400 \end{gathered}$