To solve this problem, we can use the formula for calculating the quarterly payment of a loan with compound interest:
Payment = (r * P) / (1 - (1 + r)^(-n))
where:
r = quarterly interest rate (12% / 4 = 0.03)
P = principal amount (remaining debt after down payment) = $150,000
n = total number of quarterly payments (10 years * 4 quarters per year = 40)
(1) Calculation of Quarterly Payment:
Payment = (0.03 * 150,000) / (1 - (1 + 0.03)^(-40)) = $2,365.87 (rounded to the nearest cent)
Therefore, the quarterly payment is $2,365.87.
(2) Calculation of Total Amount of Payment:
Total amount of payment = (number of payments) * (quarterly payment)
number of payments = 10 years * 4 quarters per year = 40
Total amount of payment = 40 * 2,365.87 = $94,634.80
Therefore, the total amount of payment is $94,634.80.
(3) Calculation of Total Amount of Interest Paid:
Total amount of interest paid = total amount of payment - principal amount
Total amount of interest paid = $94,634.80 - $150,000 = -$55,365.20
Note that the result is negative because the down payment ($50,000) exceeds the total amount of interest paid over the life of the loan. Therefore, in this case, the total amount of interest paid is $0, and the man ends up paying a total of $100,000 ($50,000 down payment + $50,000 in quarterly payments).