miles and nick each separately apply for and receive loans worth $5,000 apiece. miles has a very good credit score, so his loan has an apr of 7.75%, compounded monthly. nicks credit score is rather low, so his loan has an apr of 13.10% interest, compounded monthly. if both of them repay their loans over a four year period, making equal monthly payments based on their own loan, how much more will nick have paid than miles? (round all dollar values to the nearest cent.)
a. $619.68
b. $267.50
c. $1,609.57
d. $1,070.00

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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": [ "Loan Monthly Payment", "Annual Percentage Rate" ], "new_concepts": [], "current_concepts": [ "Loan Monthly Payment", "Annual Percentage Rate", "Amortized Loan" ] } ## Calculate Miles's monthly payment Using the *Loan Monthly Payment* and *Annual Percentage Rate* knowledge points $$ \begin{aligned} P &= 5000 \ r_M &= \frac{0.0775}{12} \approx 0.00645833 \ n &= 4 \times 12 = 48 \ PMT_M &= P \times \frac{r_M(1+r_M)^n}{(1+r_M)^n - 1} \ PMT_M &\approx 5000 \times \frac{0.00645833(1.00645833)^{48}}{(1.00645833)^{48} - 1} \approx 121.4124 \end{aligned} $$ ## Calculate Nick's monthly payment Using the *Loan Monthly Payment* and *Annual Percentage Rate* knowledge points $$ \begin{aligned} r_N &= \frac{0.1310}{12} \approx 0.01091667 \ PMT_N &= P \times \frac{r_N(1+r_N)^n}{(1+r_N)^n - 1} \ PMT_N &\approx 5000 \times \frac{0.01091667(1.01091667)^{48}}{(1.01091667)^{48} - 1} \approx 134.3225 \end{aligned} $$ ## Calculate total payments and difference Using the *Loan Monthly Payment* knowledge point $$ \begin{aligned} \text{Total}_M &= 121.4124 \times 48 \approx 5827.80 \ \text{Total}_N &= 134.3225 \times 48 \approx 6447.48 \ \text{Difference} &= \text{Total}_N - \text{Total}_M = 6447.48 - 5827.80 = 619.68 \end{aligned} $$

a. $619.68

b. $267.50

c. $1,609.57

d. $1,070.00

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

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Question

Explanation:

Calculate Miles's monthly payment

Calculate Nick's monthly payment

Calculate total payments and difference

Answer: