Solve the following problem:

A certificate of deposit (CD) will often result in a penalty for withdrawing funds before the maturity date. If the penalty involves two months of interest, what would be the penalty amount for early withdrawal on a CD worth [tex]\[tex]$30,000[/tex] at 8 percent annual interest?

Note: Do not round intermediate calculations.

\[
\begin{tabular}{|c|c|}
\hline
\text{Penalty Amount} & \$[/tex] \\
\hline
\end{tabular}
\]



Answer :

To determine the penalty amount for early withdrawal of a certificate of deposit (CD) worth \[tex]$30,000 with an 8% annual interest rate, where the penalty is equivalent to two months of interest, we can follow these steps: 1. Calculate the annual interest: The interest rate is given as 8%. First, we calculate the total interest earned in one year (12 months) on the CD value of \$[/tex]30,000.

[tex]\[ \text{Annual Interest} = \text{CD value} \times \text{Interest Rate} \][/tex]

Substituting the given values:

[tex]\[ \text{Annual Interest} = 30000 \times 0.08 = 2400 \text{ dollars} \][/tex]

2. Determine the monthly interest:
To find the interest earned in a single month, we divide the annual interest by 12 (since there are 12 months in a year):

[tex]\[ \text{Monthly Interest} = \frac{\text{Annual Interest}}{12} \][/tex]

Substituting the annual interest calculated:

[tex]\[ \text{Monthly Interest} = \frac{2400}{12} = 200 \text{ dollars} \][/tex]

3. Calculate the penalty amount:
The penalty involves two months of interest. Therefore, we multiply the monthly interest by 2:

[tex]\[ \text{Penalty Amount} = \text{Monthly Interest} \times 2 \][/tex]

Substituting the monthly interest calculated:

[tex]\[ \text{Penalty Amount} = 200 \times 2 = 400 \text{ dollars} \][/tex]

Thus, the penalty amount for early withdrawal on a CD worth \[tex]$30,000 at an 8 percent interest rate, given that the penalty is two months of interest, is \$[/tex]400.