Abraham's credit card has an APR of [tex]$13 \%$[/tex], calculated on the previous monthly balance, and Abraham makes a payment of [tex]$\$[/tex] 50[tex]$ every month. His credit card record for the last 7 months is shown in the table below.

\begin{tabular}{ccccccc}
\hline
\begin{tabular}{c}
End of \\
month
\end{tabular} & \begin{tabular}{c}
Previous \\
balance
\end{tabular} & \begin{tabular}{c}
New \\
charges
\end{tabular} & \begin{tabular}{c}
Payment \\
received
\end{tabular} & \begin{tabular}{c}
Finance \\
charges
\end{tabular} & \begin{tabular}{c}
Principal \\
paid
\end{tabular} & \begin{tabular}{c}
New \\
balance
\end{tabular} \\
\hline
1 & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 41.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 0.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 41.00[tex]$ \\
2 & $[/tex]\[tex]$ 41.00$[/tex] & [tex]$\$[/tex] 229.00[tex]$ & $[/tex]\[tex]$ 50.00$[/tex] & [tex]$?$[/tex] & [tex]$\$[/tex] 49.56[tex]$ & $[/tex]\[tex]$ 220.44$[/tex] \\
3 & [tex]$\$[/tex] 220.44[tex]$ & $[/tex]\[tex]$ 71.00$[/tex] & [tex]$\$[/tex] 50.00[tex]$ & $[/tex]\[tex]$ 2.39$[/tex] & [tex]$\$[/tex] 47.61[tex]$ & $[/tex]\[tex]$ 243.83$[/tex] \\
4 & [tex]$\$[/tex] 243.83[tex]$ & $[/tex]\[tex]$ 23.00$[/tex] & [tex]$\$[/tex] 50.00[tex]$ & $[/tex]\[tex]$ 2.64$[/tex] & [tex]$\$[/tex] 47.36[tex]$ & $[/tex]\[tex]$ 219.47$[/tex] \\
5 & [tex]$\$[/tex] 219.47[tex]$ & $[/tex]\[tex]$ 145.00$[/tex] & [tex]$\$[/tex] 50.00[tex]$ & $[/tex]\[tex]$ 2.38$[/tex] & [tex]$\$[/tex] 47.62[tex]$ & $[/tex]\[tex]$ 316.85$[/tex] \\
6 & [tex]$\$[/tex] 316.85[tex]$ & $[/tex]\[tex]$ 333.00$[/tex] & [tex]$\$[/tex] 50.00[tex]$ & $[/tex]\[tex]$ 3.43$[/tex] & [tex]$\$[/tex] 46.57[tex]$ & $[/tex]\[tex]$ 603.28$[/tex] \\
7 & [tex]$\$[/tex] 603.28[tex]$ & $[/tex]\[tex]$ 78.00$[/tex] & [tex]$\$[/tex] 50.00[tex]$ & $[/tex]\[tex]$ 6.54$[/tex] & [tex]$\$[/tex] 43.46[tex]$ & $[/tex]\[tex]$ 637.82$[/tex] \\
\hline
\end{tabular}

What were the finance charges in month 2?

A. [tex]$\$[/tex] 0.78[tex]$

B. $[/tex]\[tex]$ 0.44$[/tex]

C. [tex]$\$[/tex] 0[tex]$

D. $[/tex]\[tex]$ 2.39$[/tex]



Answer :

To determine the finance charges for month 2, we need to follow a systematic approach.

1. Identify the annual percentage rate (APR) and convert it to a monthly rate:
- The APR is given as 13%.
- To convert the APR to a monthly rate, divide by 12 (since there are 12 months in a year):
[tex]\[ \text{Monthly Interest Rate} = \frac{13\%}{12} = \frac{13}{100 \times 12} = \frac{13}{1200} = 0.01083333 \][/tex]

2. Determine the previous balance for month 2:
- From the table, the previous balance at the end of month 1, which becomes the previous balance for month 2, is [tex]$41.00. 3. Calculate the finance charges for month 2: - Finance charges are calculated on the previous month's balance using the monthly interest rate. - The formula to calculate finance charges is: \[ \text{Finance Charges} = \text{Previous Balance} \times \text{Monthly Interest Rate} \] - Plugging in the values: \[ \text{Finance Charges} = 41.00 \times 0.01083333 \] - Simplifying this, we obtain: \[ \text{Finance Charges} = 0.4441666666666667 \] Therefore, the finance charges for month 2 are approximately $[/tex]\[tex]$ 0.44$[/tex].

The correct answer is:
B. [tex]$\$[/tex] 0.44$