Question

Diana put $8000 in a 10-year CDpaying 5% interest compoundedmonthly. After 2 years, shewithdrew all her money, and as anearly withdrawal penalty, she paidback all the interest she madeduring the first year. How muchmoney was Diana left with?

Answer 1

Answer:

$8,430.23

Explanation:

From the statement of the problem:

• The principal amount = $8,000

,

• Interest Rate = 5%

,

• Compounding Period = 12 (Monthly)

The compound interest formula is given as:

$A(n)=P\left(1+\frac{r}{k}\right)^{nk}$

Using the compound period formula, we first, calculate the amount in her account at the end of 1 year.

$\begin{gathered} A(1)=8000\left(1+\frac{0.05}{12}\right)^{12\times1} \\ A(1)=\ 8409.30 \end{gathered}$

This means that the interest she made during the first year is:

$\text{ Interest during the first year}=8409.30-8000=\ 409.30$

Next, calculate the amount in her account at the end of the second year.

$\begin{gathered} A(2)=8000\left(1+\frac{0.05}{12}\right)^{12\times2} \\ A(2)=\ 8839.53 \end{gathered}$

Since she paid back all the interest she made during the first year, the amount Diana was left with is:

$\begin{gathered} 8839.53-409.30 \\ =8,430.23 \end{gathered}$

Diana was left with $8,430.23.