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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?

Respuesta :

Answer:

(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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