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28 February, 11:05

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?

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  1. 28 February, 12:34
    0
    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
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