calculate the monthly payment for a 5-year car loan of $23,570 at 10.43% interest, compounded monthly.
a. $247.44
b. $337.56
c. $433.88
d. $505.79

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": [ "Car Financing", "Loan Monthly Payment" ], "new_concepts": [], "current_concepts": [ "Car Financing", "Loan Monthly Payment", "Amortized Loan" ] } ## Identify the given loan parameters Using the *Car Financing* knowledge point $$ \begin{aligned} P &= \$23,570 \ r &= 10.43\% = 0.1043 \ t &= 5 \text{ years} \ n &= 12 \text{ payments per year} \end{aligned} $$ ## Calculate periodic rate and total payments Using the *Loan Monthly Payment* knowledge point $$ \begin{aligned} i &= \frac{r}{12} = \frac{0.1043}{12} \approx 0.00869167 \ N &= n \cdot t = 12 \cdot 5 = 60 \end{aligned} $$ ## Compute the monthly payment Using the *Loan Monthly Payment* knowledge point $$ \begin{aligned} M &= P \cdot \frac{i(1+i)^N}{(1+i)^N - 1} \ M &= 23570 \cdot \frac{0.00869167(1.00869167)^{60}}{(1.00869167)^{60} - 1} \ (1.00869167)^{60} &\approx 1.680696 \ M &\approx 23570 \cdot \frac{0.00869167 \cdot 1.680696}{1.680696 - 1} \ M &\approx 23570 \cdot \frac{0.014608}{0.680696} \approx 505.79 \end{aligned} $$

a. $247.44

b. $337.56

c. $433.88

d. $505.79

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

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Question

Explanation:

Identify the given loan parameters

Calculate periodic rate and total payments

Compute the monthly payment

Answer: