SOLUTION: A set of clients are seeking car loan financial advice. They are able to make monthly payments of $350 on a 6-year car loan. You know that the car dealership is able to offer them

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Question 1185594: A set of clients are seeking car loan financial advice. They are able to make monthly payments of $350 on a 6-year car loan. You know that the car dealership is able to offer them an annual interest rate of 4%. How large of a loan can they get?
Answer by ikleyn(52782) About Me  (Show Source):
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A set of clients are seeking car loan financial advice. They are able to make monthly payments of $350
on a 6-year car loan. You know that the car dealership is able to offer them an annual interest rate of 4%.
How large of a loan can they get?
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Use the formula for the monthly payment for a loan

    M = L%2A%28r%2F%281-%281%2Br%29%5E%28-n%29%29%29


where L is the loan amount; r = 0.04%2F12 is the effective interest rate per month;
n is the number of payments (same as the number of months); M is the monthly payment.


From this formula, the expression for the maximum loan is

    L = M%2F%28%28r%2F%281-%281%2Br%29%5E%28-n%29%29%29%29.


In this problem  M = $350;  r = 0.04%2F12,  n = 6*12 = 72 monthly payments.


Substitute these values into the formula and get for the maximum loan amount

    L = 350%2F%28%28%280.04%2F12%29%2F%281-%281%2B0.04%2F12%29%5E%28-72%29%29%29%29 = $22,371.11  (rounded to the closest greater cent).


ANSWER.  The maximum loan amount is $22,371.11.

Solved.