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?

Question

Business

Ximena Reynolds

14 July, 03:13

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?

+1

Answers (1)

Know the Answer?

Ariel Walters · Answer 1

Loan Value = 14,425

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