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.
