Car Prices in 2012 The National Automobile Dealers As­sociation reported that th

Question

Car Prices in 2012 The National Automobile Dealers As­sociation reported that the average retail selling price of a new vehicle was $30,303 in 2012. A person purchased a new car at the average price and financed the entire amount. Suppose that the person can only afford to pay $500 per month. Assume that the payments are made at a continuous annual rate and that interest is compounded continuously at the rate of 3.5%. (Source: The National Automobile Dealers Association,www.nada.com.)

(a) Set up a differential equation that is satisfied by the amount f(t) of money owed on the car loan at time t.

(b) How long will it take to pay off the car loan?

Explanation / Answer

b) It takes 60.6 months to pay off the loans

or approximately 5 years as it was given car price is $30303

the man can pay $500 each month so $30303/$500=60.6

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