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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": [ "Amortized Payment Calculation", "Cash Advance Interest" ], "new_concepts": [], "current_concepts": [ "Amortized Payment Calculation", "Cash Advance Interest", "Total Cost of Credit" ] } ## Identify loan parameters Using the *Amortized Payment Calculation* and *Cash Advance Interest* knowledge points $$ \begin{aligned} P &= 120.00 \ r &= \frac{0.30}{12} = 0.025 \ n &= 5 \times 12 = 60 \end{aligned} $$ ## Calculate monthly payment Using the *Amortized Payment Calculation* knowledge point $$ \begin{aligned} M &= P \frac{r(1+r)^n}{(1+r)^n - 1} \ M &= 120 \frac{0.025(1.025)^{60}}{(1.025)^{60} - 1} \ (1.025)^{60} &\approx 4.39979 \ M &\approx 120 \frac{0.025 \times 4.39979}{4.39979 - 1} \approx 120 \frac{0.10999}{3.39979} \approx 3.8824 \end{aligned} $$ ## Calculate total interest Using the *Amortized Payment Calculation* and *Cash Advance Interest* knowledge points $$ \begin{aligned} \text{Total Payments} &= M \times n \approx 3.8824 \times 60 \approx 232.94 \ \text{Total Interest} &= \text{Total Payments} - P \approx 232.94 - 120 = 112.94 \end{aligned} $$ Using standard monthly payment rounded to two decimal places: $$ \begin{aligned} M &= \$3.88 \ \text{Total Payments} &= 3.88 \times 60 = 232.80 \ \text{Total Interest} &= 232.80 - 120.00 = 112.80 \end{aligned} $$

a. $3.88

b. $112.80

c. $120.00

d. $232.80

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

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Explanation:

Identify loan parameters

Calculate monthly payment

Calculate total interest

Answer: