Answer:
The amount that will be paid to buy the car is $18,539.43.
Explanation:
This can be calculated using the following 3 steps:
Step 1: Calculation of the present of the monthly payment
Since the payments are made at the beginning of each month, this can be calculated using the formula for calculating the present value (PV) of annuity due given as follows:
PVM = P * ((1 - (1 / (1 + r))^n) / r) * (1 + r) .................................. (1)
Where;
PVM = Present value monthly payments = ?
P = Monthly withdraw = $298
r = monthly financing rate = Financing rate / Number of months in a year = 5.4% / 12 = 0.054 / 12 = 0.0045
n = number of months = 48
Substitute the values into equation (1), we have:
PVM = $298 * ((1 - (1 / (1 + 0.0045))^48) / 0.0045) * (1 + 0.0045) = $12,896.55
Step 2: Calculation of the present of the purchase amount at lease expiration
This can be calculated using the present value formula as follows:
PVP = P / (1 + r)^n .................................. (2)
Where;
PVP = Present value of the purchase amount at lease expiration = ?
P = Purchase amount at lease expiration = $7000
r = monthly financing rate = Financing rate / Number of months in a year = 5.4% / 12 = 0.054 / 12 = 0.0045
n = number of months = 48
Substitute the values into equation (2), we have:
PVP = $7000 / (1 + 0.0045)^48 = $5,642.88
Step 3: Calculation of the amount that will be paid to buy the car
This can be calculated as follows:
Amount to pay to buy car = PVM + PVP ............... (3)
Where:
PVM = Present value monthly payments = $12,896.55
PVP = $5,642.88
Substitute the values into equation (3), we have:
Amount to pay to buy car = $12,896.55 + $5,642.88 = $18,539.43
Therefore, the amount that will be paid to buy the car is $18,539.43.
