You are borrowing money to buy a car. If you can make payments of $300 per month starting one...

Question:

You are borrowing money to buy a car. If you can make payments of $300 per month starting one month from now at an interest rate of 4%, how much will you be able to borrow for the car today if you finance the amount over four years? Show work and explain.

A. $6,358.54

B. $13,067.62

C. $15,587.88

D. $13,286.65

Monthly Loan Payment:

When a loan is repaid through monthly payments, then the present value of the monthly payments, discounted at the interest rate on the loan, is equal to the amount borrowed today.

Answer and Explanation:

The answer is D.

The amount you will be able to borrow is the present value of the monthly payments, which represent an annuity. We can use the following formula to compute the present value of an annuity with periodic payment {eq}M {/eq} for {eq}T{/eq} periods, given periodic return {eq}r{/eq}:

  • {eq}\displaystyle \frac{M(1 - (1 + r)^{-T})}{r} {/eq}

The monthly payment in this question is 300, monthly interest rate is 4% / 12 = 0.33%. The loan is for 4 years, so there are 4*12 = 48 monthly payments. Applying the formula, the present value of the payment is:

  • {eq}\displaystyle \frac{300(1 - (1 + 0.33\%)^{-48})}{0.33\%} = 13,286.65 {/eq}

Learn more about this topic:

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Calculating Monthly Loan Payments

from Remedial Algebra I

Chapter 25 / Lesson 8
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