determine the monthly payment for a 36 month lease on a \$26,000 car with a residual of 71\% and an interest rate of 7.5\%.
a. \$104.87
b. \$209.44
c. \$273.08
d. \$348.38

please select the best answer from the choices provided

Question

determine the monthly payment for a 36 month lease on a \$26,000 car with a residual of 71\% and an interest rate of 7.5\%.
a. \$104.87
b. \$209.44
c. \$273.08
d. \$348.38

please select the best answer from the choices provided

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Car Lease Calculation", "Residual Value", "Money Factor" ], "current_concepts": [ "Car Lease Calculation", "Residual Value", "Money Factor" ] } ## Calculate the residual value and depreciation fee $$ \begin{aligned} \text{Capitalized Cost} &= \$26,000 \ \text{Residual Value} &= \$26,000 \times 0.71 = \$18,460 \ \text{Total Depreciation} &= \$26,000 - \$18,460 = \$7,540 \ \text{Monthly Depreciation Fee} &= \frac{\$7,540}{36} \approx \$209.4444 \end{aligned} $$ ## Calculate the money factor and monthly finance fee $$ \begin{aligned} \text{Money Factor} &= \frac{\text{Interest Rate}}{2400} = \frac{7.5}{2400} = 0.003125 \ \text{Monthly Finance Fee} &= (\text{Capitalized Cost} + \text{Residual Value}) \times \text{Money Factor} \ \text{Monthly Finance Fee} &= (\$26,000 + \$18,460) \times 0.003125 = \$44,460 \times 0.003125 = \$138.9375 \end{aligned} $$ ## Calculate the total monthly lease payment $$ \begin{aligned} \text{Total Monthly Payment} &= \text{Monthly Depreciation Fee} + \text{Monthly Finance Fee} \ \text{Total Monthly Payment} &\approx \$209.4444 + \$138.9375 = \$348.3819 \approx \$348.38 \end{aligned} $$

a. $104.87

b. $209.44

c. $273.08

d. $348.38

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Car Lease Calculation" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the residual value and depreciation fee

Calculate the money factor and monthly finance fee

Calculate the total monthly lease payment

Answer: