Suppose that you want to purchase a home for $450,000 with a 30 year mortgage at 6% interest. Suppose that you can put 40% down. Assume that the monthly cost to finance $1,000 is $6.00. What is the total amount of interest paid on the 30 year loan?
To calculate the total amount of interest paid on a 30-year loan, we need to determine the loan amount and the monthly mortgage payment. Then, we can subtract the amount borrowed from the total payment made over the loan term to find the total interest paid.
First, let's calculate the loan amount after putting 40% down on a $450,000 home.
Down payment = 40% of $450,000
Down payment = 0.4 x $450,000
Down payment = $180,000
Loan amount = Total home price - Down payment
Loan amount = $450,000 - $180,000
Loan amount = $270,000
Next, we need to calculate the monthly mortgage payment using the loan amount and the given interest rate of 6% for 30 years.
Monthly interest rate = Annual interest rate / 12 months
Monthly interest rate = 6% / 12
Monthly interest rate = 0.06 / 12
Monthly interest rate = 0.005
Number of months = Loan term in years x 12 months
Number of months = 30 years x 12 months
Number of months = 360 months
Monthly mortgage payment = Loan amount x (Monthly interest rate / (1 - (1 + Monthly interest rate)^(-Number of months)))
Monthly mortgage payment = $270,000 x (0.005 / (1 - (1 + 0.005)^(-360)))
Monthly mortgage payment ≈ $1,619.88
Now, we know the monthly mortgage payment is approximately $1,619.88.
To calculate the total interest paid over the 30-year loan term, we can subtract the loan amount from the total payment made over the loan term.
Total payment = Monthly mortgage payment x Number of months
Total payment = $1,619.88 x 360
Total payment = $583,158.80
Total interest paid = Total payment - Loan amount
Total interest paid = $583,158.80 - $270,000
Total interest paid = $313,158.80
Therefore, the total amount of interest paid on the 30-year loan would be approximately $313,158.80.