Answer:
To find the purchase price of the vehicle, we need to calculate the present value of the monthly debt payments.
Given:
Monthly debt payments (PMT) = $825
Number of years (n) = 4
Interest rate (r) = 4% compounded semi-annually
Down payment = $8,000
To calculate the purchase price, we'll use the present value formula for an annuity:
Purchase Price = PV = PMT * [(1 - (1 + r)^(-n))/(r)] - Down Payment
PV = $825 * [(1 - (1 + 0.04/2)^(-4*2))/ (0.04/2)] - $8,000
Using the formula above and performing the calculations, we find:
PV ≈ $31,444.58
Therefore, the purchase price of the vehicle is approximately $31,444.58.
To calculate the total interest paid by Magdin by the time he makes the last payment, we can subtract the total amount paid from the purchase price:
Interest Paid = (Total Amount Paid) - Purchase Price
Total Amount Paid = PMT * 12 * n
Total Amount Paid = $825 * 12 * 4 = $39,600
Interest Paid = $39,600 - $31,444.58 = $8,155.42
Therefore, Magdin will end up paying approximately $8,155.42 in interest by the time he makes the last payment.