An auto dealership is advertising that a new car with a sticker price of $19,140

Question

An auto dealership is advertising that a new car with a sticker price of $19,140 is on sale for $16,999 if you pay in cash, or you get a finance for 60 months with a monthly payment of $319. Note that 60 payments × $319 per payment = $19,140, which is the sticker price of the car. By allowing you to pay in a series of payment (starting one month from now) rather than paying $19,140 in cash, the dealer effectively makes the loan of $19,140 to you.

If you choose the financing option, what is the effective interest rate that the auto dealership charges on your loan?

Explanation / Answer

We fidn the present value of monthly payments which should be equal to cash down price.

319/(1+r) +319/(1+r)^2+...319/(1+r)^60 = 16999

SOlving for r

r = 4.94%

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