Let's break down the problem to determine which expression correctly calculates the interest Tran will be charged after the first month.
1. Determine the balance that is subject to interest:
- Tran charged [tex]$450$[/tex] to his credit card but paid [tex]$150$[/tex] by the end of his billing cycle.
- Therefore, the balance subject to interest is:
[tex]\[
\[tex]$450 - \$[/tex]150 = \$300
\][/tex]
2. Calculate the monthly interest rate:
- The APR (annual percentage rate) is \(12\%\).
- To find the monthly interest rate, we divide the APR by 12 (since there are 12 months in a year):
[tex]\[
\text{Monthly interest rate} = \frac{12\%}{12} = 1\% = 0.01
\][/tex]
3. Calculate the interest for the first month:
- The interest for the first month is calculated by multiplying the balance subject to interest (\$300) by the monthly interest rate (0.01):
[tex]\[
\text{Interest} = 0.01 \times \$300
\][/tex]
Thus, the correct expression to calculate the amount of interest Tran will be charged after the first month is:
[tex]\[
(0.01)(\$300)
\][/tex]
So, the correct option is:
[tex]\[
(0.01)(\$300)
\][/tex]
