Question

Greg has a credit card which requires a minimum monthly payment of 2.06% of the total balance. His card has an APR of 11.45%, compounded monthly.
At the beginning of May, Greg had a balance of $318.97 on his credit card. The following table shows his credit card purchases over the next few months.
Month
Cost ($)
May
46.96
May
33.51
May
26.99
June
97.24
June
112.57
July
72.45
July
41.14
July
101.84

If Greg makes only the minimum monthly payment in May, June, and July, what will his total balance be after he makes the monthly payment for July? (Assume that interest is compounded before the monthly payment is made, and that the monthly payment is applied at the end of the month. Round all dollar values to the nearest cent.)
a.
$812.86
b.
$830.31
c.
$864.99
d.
$1,039.72

Answer 1

Monthly rate = 0.1145/12 = 0.0095416666667. Interest is applied before the payment; round dollar amounts to the nearest cent each step.

May
- Start: $318.97
- Purchases: $46.96 + $33.51 + $26.99 = $107.46
- Subtotal before interest: $426.43
- After interest: 426.43×1.0095416667 = $430.50
- Minimum payment: 0.0206×430.50 = $8.87
- End of May balance: 430.50 − 8.87 = $421.63

June
- Start: $421.63
- Purchases: $97.24 + $112.57 = $209.81
- Subtotal before interest: $631.44
- After interest: 631.44×1.0095416667 = $637.46
- Minimum payment: 0.0206×637.46 = $13.13
- End of June balance: 637.46 − 13.13 = $624.33

July
- Start: $624.33
- Purchases: $72.45 + $41.14 + $101.84 = $215.43
- Subtotal before interest: $839.76
- After interest: 839.76×1.0095416667 = $847.77
- Minimum payment: 0.0206×847.77 = $17.46
- End of July balance: 847.77 − 17.46 = $830.31

Answer: $830.31 (choice b).