Question

James has a balance of $1,230 on his credit card that has an APR of 24%. He currently pays the minimum monthly payment of $30.75. If James wants to pay off his balance in 18 months, determine the monthly payment he would need to make. Choose the following modification with the least cuts to his current expenses that will allow James to pay off his balance in 18 months.
Income
Wages
$3,015.00
Expenses
Rent
$1250.00

Utilities
$432.45

Food/Clothes
$345.00

Entertainment
$255.00

Car
$360.00

Credit Card
$30.75

Cell Phone
$103.89
Net Income

$237.91

a.
James can eliminate $83 from Food/Clothes.
b.
James can eliminate $25 from Food/Clothes and $27 from Entertainment.
c.
James can eliminate $15 from Food/Clothes and $22 from Entertainment.
d.
The minimum payment is enough to pay off the balance within 24 months.

Answer 1

Monthly rate r = 24%/12 = 0.02. Using the amortization formula
Payment = r*PV / (1 - (1+r)^-n),

with PV = $1,230 and n = 18:
Payment = 0.02*(1230) / (1 - 1.02^-18)
= 24.60 / (1 - 0.7005)
≈ 24.60 / 0.2995
≈ $82.14 per month.

He currently pays $30.75, so he must increase his payment by about $82.14 − $30.75 = $51.39 per month.

Compare the options for freed cash:
- (a) frees $83 (more than needed)
- (b) frees $25 + $27 = $52 (just above $51.39)
- (c) frees $15 + $22 = $37 (not enough)
- (d) false (a $30.75 minimum would not pay off $1,230 in 24 months)

The least cuts that meet the required increase is option (b).