Question

Caitlin has a balance of $4,880 on her credit card that has an APR of 16%. She currently pays the minimum monthly payment of $105.86. If Caitlin wants to pay off her balance in 20 months, determine the monthly payment she would need to make. Choose the following modification with the least cuts to her current expenses that will allow Caitlin to pay off her balance in 20 months.
Income
Wages
$2,896.00
Expenses
Rent
$1200.00

Utilities
$212.64

Food/Clothes
$335.00

Entertainment
$346.00

Car
$490.00

Credit Card
$105.86

Cell Phone
$116.37
Net Income

$90.13

a.
Caitlin can eliminate $100 from Food/Clothes and $85 from Entertainment.
b.
Caitlin can eliminate $62 from Food/Clothes and $49 from Entertainment.
c.
Caitlin can eliminate $54 from Food/Clothes and $120 from Entertainment.
d.
The minimum payment is enough to pay off the balance within 20 months.

Answer 1

Monthly rate r = 16%/12 = 0.0133333333. Using the amortization formula
payment = r·PV / (1 − (1+r)^−n) with PV = $4,880 and n = 20:

payment ≈ (0.0133333333)(4880) / (1 − (1.0133333333)^−20) ≈ $278.88 per month.

Current payment = $105.86, so she needs an extra 278.88 − 105.86 = $173.02/month. She already has $90.13 leftover, so she must cut at least 173.02 − 90.13 = $82.89 from expenses.

Compare the options:
a) cuts = $100 + $85 = $185 (more than needed)
b) cuts = $62 + $49 = $111 (≥ $82.89, and the smallest sufficient cut)
c) cuts = $54 + $120 = $174 (more than b)
d) false

Therefore the required monthly payment is about $278.88, and the least cutting option that works is (b).