Answer:
a. The maximum price you can pay for the car is <u>$33,477.87</u>.
b. The maximum price you can pay for the car is <u>$39,411.78</u>.
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:
<u>Calculation of the Present Value (PV) of the monthly payments</u>
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
<u>Calculation of the maximum price you can pay for the car</u>
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 <u>$33,477.87</u>.
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:
<u>Calculation of the Present Value (PV) of the monthly payments</u>
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
<u>Calculation of the maximum price you can pay for the car</u>
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 <u>$39,411.78</u>.
