Question

You want to buy a new car, but you can make an initial payment of only $1,700 and can afford monthly payments of at most $725.

a. If the APR on auto loans is 9% and you finance the purchase over 36 months, what is the maximum price you can pay for the car? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. How much can you afford if you finance the purchase over 48 months? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer a.

Down payment = $1,700
Monthly payment = $725
Annual interest rate = 9.00%
Monthly interest rate = 0.75%
Period = 36 months

Present value = $1,700 + $725/1.0075 + $725/1.0075^2 + … + $725/1.0075^35 + $725/1.0075^36
Present value = $1,700 + $725 * (1 - (1/1.0075)^36) / 0.0075
Present value = $1,700 + $725 * 31.446805
Present value = $24,498.93

So, you can afford to pay $24,498.93 for the car.

Answer b.

Down payment = $1,700
Monthly payment = $725
Annual interest rate = 9.00%
Monthly interest rate = 0.75%
Period = 48 months

Present value = $1,700 + $725/1.0075 + $725/1.0075^2 + … + $725/1.0075^47 + $725/1.0075^48
Present value = $1,700 + $725 * (1 - (1/1.0075)^48) / 0.0075
Present value = $1,700 + $725 * 40.184782
Present value = $30,833.97

So, you can afford to pay $30,833.97 for the car.