Question

Julius currently pays the minimum monthly payment of $34.15 on his credit card, which has a balance of $1,289. His credit card has an APR of 20%. If Julius wants to pay off the balance in 12 months, determine the monthly payments he needs to make. Choose the following modification with the least cuts to his current expenses that will allow Julius to pay off his credit card balance in 12 months.

Income
Wages
$2,456.00
Expenses
Rent
$900.00

Utilities
$186.35

Food/Clothes
$298.00

Entertainment
$330.00

Car
$385.00

Credit Card
$34.15

Cell Phone
$89.49
Net Income

$233.01
a.
Julius can eliminate $31 from Entertainment and $55 from Food/Clothes.
b.
Julius can eliminate $80 from Entertainment and $60 from Food/Clothes.
c.
Julius can eliminate $18 from Entertainment and $32 from Food/Clothes.
d.
The minimum payment is enough to pay off the balance within 12 months.

Answer 1

Monthly rate = 20%/12 = 0.016666667.
Payment to amortize $1,289 in 12 months:
PMT = r·PV / (1 − (1+r)^−12) = 0.016666667·1289 / (1 − (1.016666667)^−12) ≈ $119.35.

He currently pays $34.15, so he needs an extra $119.35 − $34.15 = $85.20 per month.

Check options (total monthly cuts):
a) 31 + 55 = $86 → sufficient (just above $85.20)
b) 80 + 60 = $140 → sufficient but larger cut
c) 18 + 32 = $50 → insufficient
d) Minimum payment is not enough

Thus the required monthly payment is about $119.35, and option (a) is the least-cut modification that will allow payoff in 12 months.