Question

Paul is going to buy a collectible vintage painting from a local art gallery. The painting is priced at $600 in the gallery. The gallery owner does accept credit cards but prefers cash. In fact, he offers to give Paul a 5% discount if he can pay in cash. Paul doesn't have any cash but can get a cash advance on his credit card. His credit card has an APR of 16% on credit purchases and a 32% APR on cash advances. Assuming Paul wants to pay the painting off over 12 months, which of the following is true?
a.
Paul will pay a total of $696, over 12 months, if he purchases the painting with his credit card.
b.
Paul will pay a total of $653.28, over 12 months, if he purchases the painting with his credit card.
c.
Paul will pay a total of $782.40, over 12 months, if he purchases the painting with a cash advance for discounted purchase price.
d.
Paul will pay a total of $708.96, over 12 months, if he purchases the painting with a cash advance for discounted purchase price.

Answer 1

Answer: b.

Work (credit-card purchase, no cash advance):
- Monthly rate = 0.16/12 = 0.0133333333.
- Monthly payment for a 12‑month amortization = P * r / (1 − (1+r)^−12)
= 600*(0.0133333333)/(1 − (1.0133333333)^−12) ≈ $54.44.
- Total paid ≈ 54.44 * 12 ≈ $653.28.

(If he instead took a cash advance on the discounted price $570 at 32% APR, the amortized total over 12 months would be ≈ $673 — larger than $653.28.)