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?

(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.