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]
