when ivan had 4 years left in college, he took out a student loan for \$15,630. the loan has an annual interest rate of 3.9\%. ivan graduated 4 years after acquiring the loan and began repaying the loan immediately upon graduation.

according to the terms of the loan, ivan will make monthly payments for 5 years after graduation. during the 4 years he was in school and not making payments, the loan accrued simple interest.

answer each part. do not round intermediate computations, and round your answers to the nearest cent. if necessary, refer to the list of financial formulas.

(a) if ivans loan is subsidized, find his monthly payment.
subsidized loan monthly payment: \$287.23

(b) if ivans loan is unsubsidized, find his monthly payment.
unsubsidized loan monthly payment: \$332.04

Question

when ivan had 4 years left in college, he took out a student loan for \$15,630. the loan has an annual interest rate of 3.9\%. ivan graduated 4 years after acquiring the loan and began repaying the loan immediately upon graduation.

according to the terms of the loan, ivan will make monthly payments for 5 years after graduation. during the 4 years he was in school and not making payments, the loan accrued simple interest.

answer each part. do not round intermediate computations, and round your answers to the nearest cent. if necessary, refer to the list of financial formulas.

(a) if ivans loan is subsidized, find his monthly payment.
subsidized loan monthly payment: \$287.23

(b) if ivans loan is unsubsidized, find his monthly payment.
unsubsidized loan monthly payment: \$332.04

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Subsidized Loan", "Unsubsidized Loan", "Amortization Payment" ], "new_concepts": [ "Simple Interest Accrual", "Loan Amortization" ], "current_concepts": [ "Subsidized Loan", "Unsubsidized Loan", "Amortization Payment", "Simple Interest Accrual" ] } ## Calculate subsidized loan monthly payment Using the *Subsidized Loan* and *Amortization Payment* knowledge points $$ \begin{aligned} P &= 15630 \ r &= 0.039 \ n &= 12 \ t &= 5 \ i &= \frac{0.039}{12} = 0.00325 \ N &= 12 \times 5 = 60 \ PMT &= \frac{P \cdot i}{1 - (1 + i)^{-N}} \ PMT &= \frac{15630 \cdot 0.00325}{1 - (1 + 0.00325)^{-60}} \approx 287.23 \end{aligned} $$ ## Calculate unsubsidized loan balance at graduation Using the *Unsubsidized Loan* knowledge point $$ \begin{aligned} P &= 15630 \ r &= 0.039 \ t_{\text{school}} &= 4 \ I_{\text{simple}} &= P \cdot r \cdot t_{\text{school}} \ I_{\text{simple}} &= 15630 \cdot 0.039 \cdot 4 = 2438.28 \ A &= P + I_{\text{simple}} = 15630 + 2438.28 = 18068.28 \end{aligned} $$ ## Calculate unsubsidized loan monthly payment Using the *Amortization Payment* knowledge point $$ \begin{aligned} A &= 18068.28 \ i &= 0.00325 \ N &= 60 \ PMT_{\text{unsub}} &= \frac{A \cdot i}{1 - (1 + i)^{-N}} \ PMT_{\text{unsub}} &= \frac{18068.28 \cdot 0.00325}{1 - (1 + 0.00325)^{-60}} \approx 332.01 \end{aligned} $$ ## Question 1 Subsidized loan monthly payment: $287.23 ## Question 2 Unsubsidized loan monthly payment: $332.01 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Amortization Payment" ] }

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Calculate subsidized loan monthly payment

Calculate unsubsidized loan balance at graduation

Calculate unsubsidized loan monthly payment

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Question 1

Question 2