Question

124. Nina has just taken out a car loan for $12,000. She will pay an annual interest rate of 3% through a series of monthly payments for 60 months, which she pays at the end of each month. The amount of money she has left to pay on the loan at the end of the n th month can be modeled by the function f(n) = 86248 − 74248(1.0025)n for 0 ≤ n ≤ 60.

At the same time as her first payment (at the end of the first month), Nina placed $100 into a separate investment account that earns 6% per year compounded monthly. She placed $100 into the account at the end of each month thereafter. The amount of money in her savings account at the end of the n thmonth can be modeled by the function g(n) = 20000(1.005) n − 20000 for n≥ 0.
d. What does the intersection point mean in the context of this situation? Explain how you know.

Answer 1

The intersection point is the month in which she can pay for the full debt.

Explanation:

The first function f(n) describes the amount of money that she still has to pay. This is the money that she owes which is going to decrease with over the months.

The second function g(n) is the money that she has save which is going to increase with time.

The intersection point is going to be a point n in which what she owes and her savings are going to be the same. So she can use this money to pay her debt.