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Andrew is on a 30-day billing cycle. His credit card has an APR of [tex]$16.60 \%$[/tex] and computes finance charges using the previous balance method. The table below shows transactions that Andrew made in March. Based on the information in the table, what will Andrew's March finance charge be?

\begin{tabular}{|c|r|c|}
\hline
Date & Amount (\[tex]$) & Transaction \\
\hline
$[/tex]3 / 1[tex]$ & $[/tex]1,794.30[tex]$ & Beginning balance \\
\hline
$[/tex]3 / 6[tex]$ & 440.15 & Purchase \\
\hline
$[/tex]3 / 9[tex]$ & 35.65 & Purchase \\
\hline
$[/tex]3 / 22[tex]$ & 250.00 & Payment \\
\hline
$[/tex]3 / 25[tex]$ & 51.71 & Purchase \\
\hline
\end{tabular}

a. $[/tex]\[tex]$ 46.07$[/tex]
b. [tex]$\$[/tex] 28.66[tex]$
c. $[/tex]\[tex]$ 21.36$[/tex]
d. [tex]$\$[/tex] 24.82$


Sagot :

To determine Andrew's March finance charge, we will calculate the finance charge using the previous balance method. Here is a step-by-step breakdown of the calculations involved:

1. Annual Percentage Rate (APR):
- Andrew's credit card has an APR of [tex]\(16.60\%\)[/tex].

2. Converting APR to a Daily Periodic Rate:
- The APR is converted to a daily periodic rate by dividing it by the number of days in a year (365 days).
- [tex]\[ \text{Daily Periodic Rate} = \frac{APR}{365} = \frac{16.60\%}{365} = \frac{0.1660}{365} \approx 0.0004548 \][/tex]

3. Billing Cycle Length:
- Andrew’s billing cycle is 30 days.

4. Previous Balance Method:
- The finance charge is computed based on the balance at the beginning of the billing cycle. According to the problem statement, the beginning balance on March 1st was $1794.30.

5. Calculating the Finance Charge:
- The finance charge is calculated using the previous balance, the daily periodic rate, and the length of the billing cycle.
- [tex]\[ \text{Finance Charge} = \text{Previous Balance} \times \text{Daily Periodic Rate} \times \text{Billing Cycle Length} \][/tex]
- Substituting the given values:
- [tex]\[ \text{Finance Charge} = 1794.30 \times 0.0004548 \times 30 \][/tex]
- [tex]\[ \text{Finance Charge} \approx 1794.30 \times 0.013644 \approx 24.48 \][/tex]

Therefore, Andrew's March finance charge is:

[tex]\[ \boxed{24.48} \][/tex]