Hello, I need some help with calculus applied to student loans. Thank you! Payin

Question

Hello, I need some help with calculus applied to student loans. Thank you! Paying Off Student Loans Suppose that after graduation that Sarah must pay back $70,000 in student loans and that she has 15 years to do so. She has a direct subsidized undergraduate loan with an nterest rate of 4.29%, compounded monthly and this interest starts to accrue the month after she graduates. The terms of her loan are such that she will make a payment at the beginning of each month for 15 years, starting with the month she graduates. Thus, she will make a total of 15 x 12 -180 payments. Problem 11: The following will quide ww Problem 11: The following will guide you through calculating what Sarah will pay ea month. Note that this can be treated analogously to the Credit Card Debt exampl pay each e! A. Show that the future value of the Debt, D, after 15 years (n 180) is $133066.33. B. Suppose Sarah pays back P at the start of each month. Find the total amount Repaid, R, after 15 years (n 180) in terms of P C. Sarah will be out of debt when D-R. Since you know D = R when n = 180. equate the above results to find the value for P that Sarah must repay at the start of each month.

Explanation / Answer

Solution:

(A).

Future Value = $131,443.18

(B). Sarah Start with Each Start Month P

   = 70,000 / 15

= 7,778

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