when scott had 2 years left in college, he took out a student loan for \$13,425. the loan has an annual interest rate of 8.1\%. scott graduated 2 years after acquiring the loan and began repaying the loan immediately upon graduation.

according to the terms of the loan, scott will make monthly payments for 4 years after graduation. during the 2 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 scotts loan is subsidized, find his monthly payment.
subsidized loan monthly payment: \$

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

Question

when scott had 2 years left in college, he took out a student loan for \$13,425. the loan has an annual interest rate of 8.1\%. scott graduated 2 years after acquiring the loan and began repaying the loan immediately upon graduation.

according to the terms of the loan, scott will make monthly payments for 4 years after graduation. during the 2 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 scotts loan is subsidized, find his monthly payment.
subsidized loan monthly payment: \$

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

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Subsidized Loan", "Unsubsidized Loan", "Simple Interest Accrual", "Loan Amortization" ], "new_concepts": [], "current_concepts": [ "Subsidized Loan", "Unsubsidized Loan", "Simple Interest Accrual", "Loan Amortization" ] } ## Calculate subsidized loan payment Using the *Subsidized Loan* and *Loan Amortization* knowledge points $$ \begin{aligned} &P = 13425,\quad r = 0.081,\quad m = 12,\quad t = 4\ &i = \frac{0.081}{12} = 0.00675,\quad n = 4 \times 12 = 48\ &PMT = \frac{P \times i}{1 - (1 + i)^{-n}} = \frac{13425 \times 0.00675}{1 - (1.00675)^{-48}} \approx 328.32 \end{aligned} $$ ## Calculate unsubsidized loan balance at graduation Using the *Unsubsidized Loan* and *Simple Interest Accrual* knowledge points $$ \begin{aligned} &P = 13425,\quad r = 0.081,\quad t_{\text{school}} = 2\ &I = P \times r \times t_{\text{school}} = 13425 \times 0.081 \times 2 = 2174.85\ &A = P + I = 13425 + 2174.85 = 15599.85 \end{aligned} $$ ## Calculate unsubsidized loan payment Using the *Loan Amortization* knowledge point $$ \begin{aligned} &A = 15599.85,\quad i = 0.00675,\quad n = 48\ &PMT = \frac{A \times i}{1 - (1 + i)^{-n}} = \frac{15599.85 \times 0.00675}{1 - (1.00675)^{-48}} \approx 381.51 \end{aligned} $$ | No. | Answer | |---|---| | (a) | $328.32$ | | (b) | $381.51$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Loan Amortization" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate subsidized loan payment

Calculate unsubsidized loan balance at graduation

Calculate unsubsidized loan payment

Answer: