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": [ "Annual Percentage Rate", "Cash Advance Interest" ], "new_concepts": [], "current_concepts": [ "Annual Percentage Rate", "Cash Advance Interest", "Credit Card Financing Adjustments" ] } ## Calculate the credit card purchase option Using the *Annual Percentage Rate* knowledge point $$ \begin{aligned} &\text{Principal } (P) = \$600\ &\text{Annual Interest Rate } (r) = 16\% = 0.16\ &\text{Time in years } (t) = 1\text{ year}\ &\text{Total Cost} = P \times (1 + r \cdot t) = 600 \times (1 + 0.16 \times 1) = \$696 \end{aligned} $$ ## Calculate the cash advance option Using the *Cash Advance Interest* and *Annual Percentage Rate* knowledge points $$ \begin{aligned} &\text{Discounted Price } (P_{\text{cash}}) = 600 \times (1 - 0.05) = \$570\ &\text{Annual Interest Rate } (r_{\text{cash}}) = 32\% = 0.32\ &\text{Time in years } (t) = 1\text{ year}\ &\text{Total Cost} = P_{\text{cash}} \times (1 + r_{\text{cash}} \cdot t) = 570 \times (1 + 0.32 \times 1) = \$752.40 \end{aligned} $$ ## Evaluate the given options Comparing our calculated values with the choices: - Option (a) states Paul will pay a total of \$696 over 12 months if he purchases with his credit card. This matches our calculation of \$696. - Option (b) states a total of \$653.28 for the credit card purchase, which is incorrect. - Option (c) states a total of \$782.40 for the cash advance, which is incorrect. - Option (d) states a total of \$708.96 for the cash advance, which is 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", "Personal Finance", "Credit Card Financing Adjustments" ] }

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Explanation:

Calculate the credit card purchase option

Calculate the cash advance option

Evaluate the given options

Answer: