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Mindy's credit card has an APR of [tex]$15 \%$[/tex], calculated on the previous monthly balance, and Mindy makes a payment of [tex][tex]$\$[/tex] 50$[/tex] every month. Her 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]$ 0.00$[/tex] & [tex]$\$[/tex] 45.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 0.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 45.00[tex]$ \\
2 & $[/tex]\[tex]$ 45.00$[/tex] & [tex]$\$[/tex] 193.00[tex]$ & $[/tex]\[tex]$ 50.00$[/tex] & [tex]$?$[/tex] & [tex]$\$[/tex] 49.44[tex]$ & $[/tex]\[tex]$ 188.56$[/tex] \\
3 & [tex]$\$[/tex] 188.56[tex]$ & $[/tex]\[tex]$ 90.00$[/tex] & [tex]$\$[/tex] 50.00[tex]$ & $[/tex]\[tex]$ 2.36$[/tex] & [tex]$\$[/tex] 47.64[tex]$ & $[/tex]\[tex]$ 230.92$[/tex] \\
4 & [tex]$\$[/tex] 230.92[tex]$ & $[/tex]\[tex]$ 77.00$[/tex] & [tex]$\$[/tex] 50.00[tex]$ & $[/tex]\[tex]$ 2.89$[/tex] & [tex]$\$[/tex] 47.11[tex]$ & $[/tex]\[tex]$ 260.81$[/tex] \\
5 & [tex]$\$[/tex] 260.81[tex]$ & $[/tex]\[tex]$ 38.00$[/tex] & [tex]$\$[/tex] 50.00[tex]$ & $[/tex]\[tex]$ 3.26$[/tex] & [tex]$\$[/tex] 46.74[tex]$ & $[/tex]\[tex]$ 252.07$[/tex] \\
6 & [tex]$\$[/tex] 252.07[tex]$ & $[/tex]\[tex]$ 227.00$[/tex] & [tex]$\$[/tex] 50.00[tex]$ & $[/tex]\[tex]$ 3.15$[/tex] & [tex]$\$[/tex] 46.85[tex]$ & $[/tex]\[tex]$ 432.22$[/tex] \\
7 & [tex]$\$[/tex] 432.22[tex]$ & $[/tex]\[tex]$ 88.00$[/tex] & [tex]$\$[/tex] 50.00[tex]$ & $[/tex]\[tex]$ 5.40$[/tex] & [tex]$\$[/tex] 44.60[tex]$ & $[/tex]\[tex]$ 475.62$[/tex] \\
\hline
\end{tabular}

What were the finance charges in month 2?


Sagot :

To solve for the finance charges in month 2, we need to follow these steps:

1. Identify the previous balance for month 2:
The previous balance is \[tex]$45.00. 2. Identify the APR: The APR (Annual Percentage Rate) is 15%. 3. Convert APR to a monthly rate: Since APR is the annual percentage rate, we need to convert it to a monthly rate. The monthly rate is calculated as: \[\text{Monthly Rate} = \frac{APR}{12} = \frac{15\%}{12} = \frac{0.15}{12}\] 4. Calculate the finance charge: The monthly finance charge is calculated based on the previous balance and the monthly rate. This is given by: \[\text{Finance Charge} = \text{Previous Balance} \times \text{Monthly Rate}\] \[\text{Finance Charge} = \$[/tex]45.00 \times \left(\frac{0.15}{12}\right)\]

5. Compute the exact finance charge:
[tex]\[\text{Finance Charge} = \$45.00 \times 0.0125\][/tex]
[tex]\[\text{Finance Charge} = \$0.5625\][/tex]

Thus, the finance charges in month 2 are \$0.5625.