Question

Maya’s credit card has an APR of 11.84% and a billing cycle of 30 days. The table below shows her transactions with that credit card in the month of September.

Date
Amount ($)
Transaction
9/1
395.61
Beginning balance
9/8
24.13
Purchase
9/13
68.57
Payment
9/26
31.77
Purchase

Find Maya’s finance charge for September using the previous balance method, the adjusted balance method, and the daily balance method. Among those three possible finance charges, what is the value of the one which is neither lowest nor highest?
a.
$3.79
b.
$3.90
c.
$3.68
d.
$4.45

Answer 1

Compute the periodic rates first:
- Monthly rate = APR/12 = 0.1184/12 = 0.0098666667.
- Daily-method factor for a 30-day cycle = APR*(30/365) = 0.1184*(30/365) = 0.0097328767.

Transactions by day segments (9/1–9/30):
- 9/1–9/7 (7 days): balance = 395.61 → 395.61×7 = 2,769.27
- 9/8–9/12 (5 days): balance = 395.61+24.13 = 419.74 → 419.74×5 = 2,098.70
- 9/13–9/25 (13 days): balance after payment = 419.74−68.57 = 351.17 → 351.17×13 = 4,565.21
- 9/26–9/30 (5 days): balance after purchase = 351.17+31.77 = 382.94 → 382.94×5 = 1,914.70
Sum of daily balances = 11,347.88 → average daily balance = 11,347.88/30 = 378.2626667

Now the three methods:

1) Previous-balance method:
Finance charge = beginning balance × monthly rate
= 395.61 × 0.0098666667 ≈ 3.90335 → $3.90

2) Adjusted-balance method (previous balance minus payments during cycle, then monthly rate):
Adjusted balance = 395.61 − 68.57 = 327.04
Finance charge = 327.04 × 0.0098666667 ≈ 3.227 → $3.23

3) Daily (average daily) balance method:
Finance charge = average daily balance × APR × (30/365)
= 378.2626667 × 0.1184 × (30/365) ≈ 378.2626667 × 0.0097328767 ≈ 3.683 → $3.68

The three charges are $3.90, $3.23, and $3.68. The one that is neither lowest nor highest (the middle value) is $3.68.

Answer: c. $3.68