Explanation The loan provided to the undergraduate students who are in need of financial help is termed as a subsidized loan. It is estimated by subtracting the family contribution from the student’s attendance cost. The interest is not accrued at the time when the student is studying. The unsubsidized loans are the loans which are provided both to the graduates and undergraduates. This loan is not based on the financial requirements of the students. In this type of loan, accrued interest is added at the time the student is pursuing graduation. The interest rate on the subsidized and unsubsidized loan is same. Let us consider the same amount of loan in both the subsidized and unsubsidized loan situations. The amount of borrowing is $ 3 , 500 . The interest rate for both the situations is same say 4.29 % for the term of 4 years. The monthly payment in both the cases of subsidized and unsubsidized loan is calculated by using the formulae given below: R = P i 1 − ( 1 + i ) − n Here, R is the monthly payment, P is the total cost, i is the monthly rate of interest and n is the number of payments. The monthly rate of interest i is calculated below: i = ( 4.29 100 ) ⋅ ( 1 12 ) = 0.0429 ⋅ 1 12 = 0.003575 Thus, the monthly rate of interest i is 0.003575 . The number of payments n is calculated below: n = 4 × 12 = 48 Thus, the number of payments n are 48 . So, the monthly payment is calculated below: R = P i 1 − ( 1 + i ) − n = $ 3 , 500 × 0.003575 1 − ( 1 + 0.003575 ) − 48 = $ 12.5125 1 − ( 1.003575 ) − 48 = $ 12.5125 1 − 0.84257382 Further simplified as: R = $ 12.5125 0.15742618 = $ 79.48 = $ 79 Thus, the monthly payment in both cases ( R ) is $ 79 . Now, the interest paid during the years of the loan and the monthly payment along with the repayment amount needs to be calculated step by step. First, the interest amount for the duration of 4 years is to be calculated when the student is still in the years of his graduation. In case of a subsidized loan, the interest is not charged till the student is in school or is yet to be graduated. Thus, in this case, the amount owed at the time of graduation is same that is $ 3 , 500 and no interest is accrued. In case of an unsubsidized loan, the interest is to be compounded for 4 years. In order to calculate the amount of interest, the amount or balance to be owed at the time of graduation is required. The amount owed at the time of graduation can be calculated by using the formulae of compound interest given below: A = P ( 1 + r n ) n t Where A is the future amount of lump sum, P is principal amount, r is anuual interest rate, t is number of years, n is the number of periods

Pearson eText for Mathematics with Applications In the Management, Natural, and Social Sciences -- Instant Access (Pearson+)

12th Edition

ISBN: 9780137504381

Author: Margaret Lial, Thomas Hungerford

Publisher: PEARSON+

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Chapter 5, Problem 1EP

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The interest rate of subsidized and unsubsidized loans. The monthly payment and repayment amount also need to be calculated in both the cases.

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Chapter 5, Problem 6CE

Chapter 5, Problem 2EP

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