You want to buy a new car, but you can make an initial payment of only $1,200 and can afford monthly payments of at most $850. a. If the APR on auto loans is 12% and you finance the purchase over 48 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 60 months? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

a. The maximum price you can pay for the car is $33,477.87.

b. The maximum price you can pay for the car is $39,411.78.

Explanation:

a. If the APR on auto loans is 12% and you finance the purchase over 48 months, what is the maximum price you can pay for the car? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

This can be determined as follows:

Calculation of the Present Value (PV) of the monthly payments

To calculate, the formula for calculating the present value of an ordinary annuity is used as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value of the monthly payments = ?

P = Monthly payment = $850

r = monthly interest rate = annual percentage rate (APR) / 12 = 12% / 12 = 1%, or 0.01

n = number of months = 48

Substitute the values into equation (1) to have:

PV = $850 * ((1 - (1 / (1 + 0.01))^48) / 0.01)

PV = $850 * 37.9739594934803

PV = $32,277.87

Calculation of the maximum price you can pay for the car

Given in the question is initial payment of only $1,200.

The present value of the monthly payments calculated above is $32,277.87.

Therefore, we have:

Maximum price = Initial payment + Present value of the monthly payments = $1,200 + $32,277.87 = $33,477.87

Therefore, the maximum price you can pay for the car is $33,477.87.

b. How much can you afford if you finance the purchase over 60 months? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

This can also be determined as follows:

Calculation of the Present Value (PV) of the monthly payments

To calculate this, we use equation (1) in part (a) above, change number f months to 60 and proceed as follows:

PV = Present value of the monthly payments = ?

P = Monthly payment = $850

r = monthly interest rate = annual percentage rate (APR) / 12 = 12% / 12 = 1%, or 0.01

n = number of months = 60

Substitute the values into equation (1) to have:

PV = $850 * ((1 - (1 / (1 + 0.01))^60) / 0.01)

PV = $850 * 44.9550384062241

PV = $38,211.78

Calculation of the maximum price you can pay for the car

Given in the question is initial payment of only $1,200.

The present value of the monthly payments calculated above is $38,211.78.

Therefore, we have:

Maximum price = Initial payment + Present value of the monthly payments = $1,200 + $38,211.78 = $39,411.78

Therefore, the maximum price you can pay for the car is $39,411.78.

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