Question

Cynthia had a credit card with a 17% APR and a $3,265 balance. She had budgeted to have the credit card paid off in 24 months. But after missing a single monthly payment, Cynthia’s credit card company has increased her interest rate to 21%. How much extra will Cynthia have to pay in finance charges (interest) because of the increase in her APR if she still pays off the credit card in 24 months?
a.
$152.16
b.
$272.08
c.
$609.32
d.
$761.48

Answer 1

Answer: a) $152.16

Work (brief):
- Monthly rates: r1 = 0.17/12 = 0.0141666667, r2 = 0.21/12 = 0.0175.
- Monthly payment for an amortizing loan: A = P·r / (1 − (1+r)^−n), with P = 3265, n = 24.

Compute at 17%:
- A1 ≈ 3265·0.0141667 / (1 − (1.0141667)^−24) ⇒ A1 ≈ $161.64
- Total paid ≈ 24·A1 ≈ $3,874.32 → interest ≈ $3,874.32 − $3,265 = $609.32

Compute at 21%:
- A2 ≈ 3265·0.0175 / (1 − (1.0175)^−24) ⇒ A2 ≈ $167.73
- Total paid ≈ 24·A2 ≈ $4,026.48 → interest ≈ $4,026.48 − $3,265 = $761.48

Extra interest = $761.48 − $609.32 = $152.16.