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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 :

GinnyAnswer
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]

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