bianca took out a \$2,600 unsubsidized stafford loan. she will be attending school for four years, and she wishes to have the loan paid off five years before its normal ten-year duration is finished. the loan has an interest rate of 6.2\%, compounded monthly. how much will she have to pay monthly to avoid interest capitalization?
a. \$12.40
b. \$19.29
c. \$13.43
d. \$17.36

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": [ "Interest Capitalization", "Student Loans" ], "new_concepts": [], "current_concepts": [ "Student Loans", "Interest Capitalization", "Compound Interest" ] } ## Identify the goal and parameters Using the **Student Loans** knowledge point $$ \begin{aligned} &\text{Principal } (P) = \$2,600\ &\text{Annual Interest Rate } (r) = 6.2\% = 0.062\ &\text{Compounding periods per year } (n) = 12 \end{aligned} $$ ## Calculate the monthly interest payment Using the **Interest Capitalization** knowledge point $$ \begin{aligned} &I_{\text{monthly}} = P \times \frac{r}{n}\ &I_{\text{monthly}} = 2600 \times \frac{0.062}{12}\ &I_{\text{monthly}} \approx 13.4333 \end{aligned} $$ ## Match with the options Using the **Interest Capitalization** knowledge point $$ \begin{aligned} &\text{Monthly payment} \approx \$13.43\ &\text{Matches option (c)} \end{aligned} $$

a. $12.40

b. $19.29

c. $13.43

d. $17.36

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Interest Capitalization" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the goal and parameters

Calculate the monthly interest payment

Match with the options

Answer: