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
$[/tex]3/6[tex]$ & $[/tex]440.15[tex]$ & Purchase \\
\hline
$[/tex]3/9[tex]$ & $[/tex]35.65[tex]$ & Purchase \\
\hline
$[/tex]3/22[tex]$ & $[/tex]250.00[tex]$ & Payment \\
\hline
$[/tex]3/25[tex]$ & $[/tex]51.71[tex]$ & Purchase \\
\hline
\end{tabular}

a. $[/tex]\[tex]$ 46.07$[/tex]

b. [tex]$\$[/tex] 28.66[tex]$

c. $[/tex]\[tex]$ 2136$[/tex]

d. [tex]$\$[/tex] 24.82$



Answer :

To determine Andrew's March finance charge using the previous balance method with an APR (Annual Percentage Rate) of 16.60%, we'll follow these steps:

1. Identify the information provided:
- APR (Annual Percentage Rate): 16.60%
- Billing cycle: 30 days
- Previous balance on March 1: [tex]$1,794.30 - Transactions: - March 6: Purchase of $[/tex]440.15
- March 9: Purchase of [tex]$35.65 - March 22: Payment of $[/tex]250.00
- March 25: Purchase of [tex]$51.71 2. Understand the previous balance method: - The finance charge is based on the balance at the start of the billing cycle, regardless of transactions during the billing cycle. 3. Calculate the finance charge: - Convert the APR to a decimal by dividing by 100: \( 16.60\% / 100 = 0.166 \) - Calculate the daily periodic rate by dividing the APR by the number of days in a year (365): \( 0.166 / 365 \approx 0.0004548 \) - The daily periodic rate needs to be multiplied by the number of days in the billing cycle (30 days) and the previous balance ($[/tex]1,794.30):
[tex]\[ \text{Finance charge} = \text{Daily periodic rate} \times \text{Billing cycle days} \times \text{Previous balance} \][/tex]
[tex]\[ \text{Finance charge} = 0.0004548 \times 30 \times 1794.30 \][/tex]

4. Compute the actual finance charge:
- Step-by-step calculation:
- Daily periodic rate: [tex]\( 0.0004548 \)[/tex]
- Previous balance: [tex]$1,794.30 - Billing cycle days: 30 - Daily periodic rate × Previous balance: \( 0.0004548 \times 1794.30 \approx 0.8159 \) - Finance charge: \( 0.8159 \times 30 \approx 24.48 \) Thus, Andrew's March finance charge, calculated based on the previous balance method, is: \[ \boxed{24.48} \] Given the choices: a. $[/tex]\[tex]$ 46.07$[/tex]
b. [tex]$\$[/tex] 28.66[tex]$ c. $[/tex]\[tex]$ 21.36$[/tex]
d. [tex]$\$[/tex] 24.82$

The closest match to our calculated value is:

[tex]\[ \boxed{24.82} \][/tex]