ralph is leasing a \$32,000 car for 36 months. the terms of his lease include an 8.5\% interest rate (money factor of 0.00354) and a residual value of 72\%. determine ralphs approximate monthly lease payment.
a. \$145.00
b. \$230.40
c. \$248.89
d. \$443.73

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

Question

ralph is leasing a \$32,000 car for 36 months. the terms of his lease include an 8.5\% interest rate (money factor of 0.00354) and a residual value of 72\%. determine ralphs approximate monthly lease payment.
a. \$145.00
b. \$230.40
c. \$248.89
d. \$443.73

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": [ "Car Financing" ], "new_concepts": [ "Car Lease Calculation", "Residual Value", "Money Factor" ], "current_concepts": [ "Car Financing", "Car Lease Calculation", "Residual Value", "Money Factor" ] } ## Calculate residual value and depreciation Using the *Car Financing* knowledge point $$ \begin{aligned} &\text{Capitalized Cost (Cap Cost)} = \$32,000\ &\text{Residual Value Rate} = 72\% = 0.72\ &\text{Residual Value} = \$32,000 \times 0.72 = \$23,040\ &\text{Total Depreciation} = \$32,000 - \$23,040 = \$8,960 \end{aligned} $$ ## Calculate monthly depreciation payment Using the *Car Financing* knowledge point $$ \begin{aligned} &\text{Lease Term} = 36\text{ months}\ &\text{Monthly Depreciation} = \frac{\$8,960}{36} \approx \$248.8889 \end{aligned} $$ ## Calculate monthly finance charge Using the *Car Financing* knowledge point $$ \begin{aligned} &\text{Money Factor} = 0.00354\ &\text{Monthly Finance Charge} = (\text{Cap Cost} + \text{Residual Value}) \times \text{Money Factor}\ &\text{Monthly Finance Charge} = (\$32,000 + \$23,040) \times 0.00354 = \$55,040 \times 0.00354 \approx \$194.8416 \end{aligned} $$ ## Calculate total monthly lease payment Using the *Car Financing* knowledge point $$ \begin{aligned} &\text{Monthly Lease Payment} = \text{Monthly Depreciation} + \text{Monthly Finance Charge}\ &\text{Monthly Lease Payment} \approx \$248.8889 + \$194.8416 = \$443.7305 \approx \$443.73 \end{aligned} $$

a. $145.00

b. $230.40

c. $248.89

d. $443.73

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

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Question

Explanation:

Calculate residual value and depreciation

Calculate monthly depreciation payment

Calculate monthly finance charge

Calculate total monthly lease payment

Answer: