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%.

Step-by-step 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+(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+(r)/(n))^(nt) \\ A=4000(1+(0.16)/(1))^((1)) \\ A=4000(1.16) \\ A=4640 \end{gathered}`

(b):

For 2 years:

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=4000(1+(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}`