Tran has a credit card with a spending limit of [tex] \[tex]$2000 [/tex] and an APR (annual percentage rate) of [tex] 12\% [/tex]. During the first month, Tran charged [tex] \$[/tex]450 [/tex] and paid [tex] \$150 [/tex] of that in his billing cycle. Which expression will find the amount of interest Tran will be charged after the first month?

A. [tex] (0.01)(\$300) [/tex]
B. [tex] (0.01)(\$450) [/tex]
C. [tex] (0.12)(\$300) [/tex]
D. [tex] (0.12)(\$450) [/tex]



Answer :

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]