gary has a credit card with an apr of 13.57%, compounded monthly. he would like to pay off the $1,847.42 card balance over the course of two and a half years by making identical monthly payments. assuming that he makes no additional purchases on his card, how much must gary pay every month to reach his goal? (round all dollar values to the nearest cent.)
a. $72.96
b. $137.45
c. $61.58
d. $86.29

Question

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": [ "Annual Percentage Rate", "Loan Monthly Payment" ], "new_concepts": [ "Credit Card Amortization" ], "current_concepts": [ "Annual Percentage Rate", "Loan Monthly Payment", "Credit Card Amortization" ] } ## Identify given parameters Using the *Annual Percentage Rate* knowledge point $$ \begin{aligned} P &= 1847.42 \ r &= \frac{0.1357}{12} \approx 0.011308333 \ n &= 2.5 \times 12 = 30 \end{aligned} $$ ## Calculate monthly payment Using the *Loan Monthly Payment* knowledge point $$ \begin{aligned} M &= P \frac{r(1+r)^n}{(1+r)^n - 1} \ M &= 1847.42 \frac{0.011308333(1.011308333)^{30}}{(1.011308333)^{30} - 1} \ (1.011308333)^{30} &\approx 1.4019818 \ M &\approx 1847.42 \frac{0.011308333 \times 1.4019818}{1.4019818 - 1} \ M &\approx 1847.42 \frac{0.01585416}{0.4019818} \ M &\approx 1847.42 \times 0.03943999 \approx 72.86 \end{aligned} $$ ## Match with closest option Using the *Loan Monthly Payment* knowledge point $$ \begin{aligned} M &\approx 72.96 \quad (\text{Option a}) \end{aligned} $$

(a) $72.96

(b) $137.45

(c) $61.58

(d) $86.29

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Loan Monthly Payment" ] }

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Question

Explanation:

Identify given parameters

Calculate monthly payment

Match with closest option

Answer: