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 doesnt 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.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Cash Advance Interest", "Credit Card Purchase vs Cash Advance" ], "new_concepts": [ "Credit Card Amortization Formula" ], "current_concepts": [ "Cash Advance Interest", "Credit Card Purchase vs Cash Advance", "Credit Card Amortization Formula" ] } ## Calculate credit card purchase option Using the *Credit Card Purchase vs Cash Advance* knowledge point $$ \begin{aligned} &P = \$600,\quad r = \frac{0.16}{12},\quad n = 12\ &M = P \frac{r(1+r)^n}{(1+r)^n - 1} = 600 \frac{\frac{0.16}{12}(1+\frac{0.16}{12})^{12}}{(1+\frac{0.16}{12})^{12} - 1} \approx 54.44\ &\text{Total} = 12 \times 54.44 = \$653.28 \end{aligned} $$ ## Calculate cash advance option Using the *Cash Advance Interest* knowledge point $$ \begin{aligned} &P_{\text{cash}} = 600 \times (1 - 0.05) = \$570\ &r_{\text{cash}} = \frac{0.32}{12},\quad n = 12\ &M_{\text{cash}} = 570 \frac{\frac{0.32}{12}(1+\frac{0.32}{12})^{12}}{(1+\frac{0.32}{12})^{12} - 1} \approx 56.03\ &\text{Total}_{\text{cash}} = 12 \times 56.03 = \$672.36 \end{aligned} $$ ## Compare calculated values with options Comparing the calculated totals with the given options: - Option (a) states the credit purchase total is \$696 (incorrect). - Option (b) states the credit purchase total is \$653.28 (correct). - Option (c) states the cash advance total is \$782.40 (incorrect). - Option (d) states the cash advance total is \$708.96 (incorrect).

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.

{ "subject": "Business", "question_type": "Multiple Choice", "knowledge_point": [ "Business", "Finance", "Credit Card Purchase vs Cash Advance" ] }

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Explanation:

Calculate credit card purchase option

Calculate cash advance option

Compare calculated values with options

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