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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": [ "Lifetime Cost Calculation", "Amortized Payment Calculation" ], "new_concepts": [ "Operating Cost Analysis" ], "current_concepts": [ "Lifetime Cost Calculation", "Amortized Payment Calculation", "Operating Cost Analysis" ] } ## Calculate total electricity cost Using the *Lifetime Cost Calculation* knowledge point $$ \begin{aligned} \text{Total Days} &= 7 \times 365 + 2 \times 366 = 2555 + 732 = 3287\text{ days} \ \text{Electricity Cost} &= 3287 \times 0.19 = 624.53\text{ dollars} \end{aligned} $$ ## Calculate monthly credit card payment Using the *Amortized Payment Calculation* knowledge point $$ \begin{aligned} P &= 745 \ r &= \frac{0.1684}{12} \approx 0.01403333 \ n &= 48 \ M &= P \times \frac{r(1+r)^n}{(1+r)^n - 1} \ M &\approx 745 \times \frac{0.01403333(1.01403333)^{48}}{(1.01403333)^{48} - 1} \approx 21.43\text{ dollars} \end{aligned} $$ ## Calculate total financing cost Using the *Lifetime Cost Calculation* knowledge point $$ \begin{aligned} \text{Total Financing Cost} &= 48 \times 21.43 = 1028.64\text{ dollars} \end{aligned} $$ ## Calculate lifetime cost and percentage Using the *Lifetime Cost Calculation* knowledge point $$ \begin{aligned} \text{Lifetime Cost} &= 1028.64 + 624.53 = 1653.17\text{ dollars} \ \text{Percentage} &= \frac{624.53}{1653.17} \times 100\% \approx 37.77\% \end{aligned} $$

(a) 59.17%

(b) 18.48%

(c) 66.99%

(d) 37.77%

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Lifetime Cost Calculation" ] }

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Explanation:

Calculate total electricity cost

Calculate monthly credit card payment

Calculate total financing cost

Calculate lifetime cost and percentage

Answer: