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2 November, 07:03

A college student receives an interest-free loan of $9,400 from a relative. The student will repay $200 per month until the loan is paid off.

(a) Express the amount P (in dollars) remaining to be paid in terms of time t (in months). (Give your answer in slope-intercept form.)

(b) After how many months will the student owe $5000?

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  1. 2 November, 07:27
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    (a) P = - 200 T + 9,400

    (b) After 22 months the student will owe $5000.

    Step-by-step explanation:

    Here, the amount loaned out to the student = $9,400

    The installment amount of each month = $200

    (a) P : Amount remaining to be paid

    T: time in months

    Now, the remaining amount = Actual amount - Amount paid in T months

    or, P = 9,400 - $200 (T)

    ⇒ P = - 200 T + 9,400 (y = mx + C form)

    (b) The remaining amount left = $5000

    As we know, P = 9,400 - $200 (T)

    ⇒ 5,000 = 9,400 - 200 T

    ⇒200 T = 9,400 - 5,000 = 4,400

    ⇒ T = 4400/200 = 22

    or T = 22 Months

    Hence, After 22 months the student will owe $5000.
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