Question

A student has a job that leaves her with $500 per month in disposable income. She decides that she will use the money to buy a car. Before looking for a car, she arranges a 100% loan whose terms are $500 per month for 36 months at 15% annual interest.

Required:
1. What is the maximum car purchase price that she can afford with her loan?

Answer 1

Loan Value = 14,425

Step-by-step explanation:

A fix Payment for a specified period of time is called annuity. The discounting of these payment on a specified rate is known as present value of annuity. In this question the monthly payment of $500 for 36 months at 15% per year is an annuity.

Formula for Present value of annuity is as follow

PV of annuity = P x [ ( 1- ( 1+ r )^-n ) / r ]

As the Present value of annuity is the value of loan

Loan Value = P x [ ( 1- ( 1+ r )^-n ) / r ]

Loan Value = $500 x [ ( 1- ( 1+ 15%/12 )^-36 ) / 15%12 ]

Loan Value = $14,424.6

Loan Value = $14,425