Question

Antonio's credit card has an APR of 16.65%, and it calculates his finance charge by using the daily balance method and a 30-day billing cycle. On June 1st, Antonio had a balance of $811.67. During the month of June, he made a payment of $110.16 and a purchase of $84.04. How much greater will his June finance charge be if the purchase occurred on June 5th and the payment occurred on June 23rd than it would be if the payment occurred on June 5th and the purchase occurred on June 23rd?
a.
$0.44
b.
$1.59
c.
$4.96
d.
$0.36

Answer 1

Daily rate = 16.65%/365 = 0.1665/365 ≈ 0.00045616438.

Compute sum of daily balances (30 days) in each case (balance after transactions on that day):

Case 1: purchase June 5, payment June 23
- Days 1–4 (4 days): 811.67
- Days 5–22 (18 days): 811.67 + 84.04 = 895.71
- Days 23–30 (8 days): 895.71 − 110.16 = 785.55
Sum = 4(811.67) + 18(895.71) + 8(785.55) = 25,653.86

Case 2: payment June 5, purchase June 23
- Days 1–4 (4 days): 811.67
- Days 5–22 (18 days): 811.67 − 110.16 = 701.51
- Days 23–30 (8 days): 701.51 + 84.04 = 785.55
Sum = 4(811.67) + 18(701.51) + 8(785.55) = 22,158.26

Difference in sum of daily balances = 25,653.86 − 22,158.26 = 3,495.60

Difference in finance charge = daily rate × difference = (0.1665/365) × 3,495.60 ≈ $1.595 ≈ $1.59.

Answer: b. $1.59.