Answer:
$2.15
Step-by-step explanation:
To determine the finance charge on the average daily balance of a credit card, we can use the Average Daily Balance Method.
The cardholder has an initial balance of $100. They make a $50 purchase on day 4 of the billing period, raising their balance to $200, and then make a payment of $150 on day 21, lowering their balance to $50 for the last 10 days of the billing period.
To find the average daily balance, divide the sum of the balances at the end of each day by the number of days in the billing cycle:
[tex]\textsf{Average daily balance}=\dfrac{\$150 \times 3 + \$200 \times 17+\$50 \times 10}{30}\\\\\\\textsf{Average daily balance}=\dfrac{\$450+\$3400+\$500}{30}\\\\\\\textsf{Average daily balance}=\dfrac{\$4350}{30}\\\\\\\textsf{Average daily balance}=\$145\\\\\\[/tex]
The given annual interest rate (APR) is 18%. To translate this into the daily periodic rate, divide the APR by the number of days in a year:
[tex]\textsf{Daily periodic rate}=\dfrac{0.18}{365}[/tex]
Finally, to compute the finance charge for the full 30-day billing period, multiply the average daily balance of $145 by the daily periodic rate and then by the number of days in the billing period:
[tex]\textsf{Finance charge}=\$145 \times \dfrac{0.18}{365}\times 30\\\\\\\textsf{Finance charge}=\$2.14520547945...\\\\\\\textsf{Finance charge}=\$2.15[/tex]
Therefore, the finance charge is:
[tex]\Large\boxed{\boxed{\$2.15}}[/tex]
