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 interest 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 × 12 = 180 payments.
A. Show that the future value of the Debt, D, after 15 years (n = 180) is $132,592.31.
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.