bobs car needs a new transmission, a repair that will cost $1,763.00. bob does not have enough money in his savings account to cover the cost of the repair. to make matters worse, bobs mechanic, who works out of his home, is unable to accept credit cards. bob is hesitant to take out a cash advance on his credit card knowing that it will take him 12 months to pay of the balance and that a cash advance comes with a 30% interest rate. if bob uses a cash advance to pay for the repairs, how much extra will he have to pay in interest?
a. $146.92
b. $171.87
c. $299.44
d. $528.90

please select the best answer from the choices provided
a
b
c
d

Question

bobs car needs a new transmission, a repair that will cost $1,763.00. bob does not have enough money in his savings account to cover the cost of the repair. to make matters worse, bobs mechanic, who works out of his home, is unable to accept credit cards. bob is hesitant to take out a cash advance on his credit card knowing that it will take him 12 months to pay of the balance and that a cash advance comes with a 30% interest rate. if bob uses a cash advance to pay for the repairs, how much extra will he have to pay in interest?
a. $146.92
b. $171.87
c. $299.44
d. $528.90

please select the best answer from the choices provided
a
b
c
d

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Amortized Payment Calculation", "Total Cost of Credit" ], "new_concepts": [ "Cash Advance Interest" ], "current_concepts": [ "Amortized Payment Calculation", "Total Cost of Credit", "Cash Advance Interest" ] } ## Identify the given parameters Using the *Amortized Payment Calculation* knowledge point $$ \begin{aligned} P &= 1763.00 \ r &= 0.30 \ n &= 12 \ i &= \frac{0.30}{12} = 0.025 \end{aligned} $$ ## Calculate the monthly payment Using the *Amortized Payment Calculation* knowledge point $$ \begin{aligned} M &= P \frac{i(1+i)^n}{(1+i)^n - 1} \ M &= 1763 \cdot \frac{0.025(1.025)^{12}}{(1.025)^{12} - 1} \ (1.025)^{12} &\approx 1.3448888 \ M &\approx 1763 \cdot \frac{0.025 \cdot 1.3448888}{1.3448888 - 1} \ M &\approx 1763 \cdot \frac{0.0336222}{0.3448888} \ M &\approx 1763 \cdot 0.0974871 \approx 171.8697 \end{aligned} $$ ## Calculate the total interest paid Using the *Total Cost of Credit* knowledge point $$ \begin{aligned} \text{Total Payments} &= 12 \cdot 171.8697 \approx 2062.44 \ \text{Total Interest} &= \text{Total Payments} - P \ \text{Total Interest} &\approx 2062.44 - 1763.00 = 299.44 \end{aligned} $$

a. $146.92

b. $171.87

c. $299.44

d. $528.90

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Amortized Payment Calculation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Calculate the monthly payment

Calculate the total interest paid

Answer: