Suppose that you want to purchase a home for $450,000 with a 30 year mortgage at 6% interest. Suppose that you can put 20% 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?
Po = 450,000 - 0.20*450,000 = $360,000.
Pt = (360,000/1000) * 6.00 * 360mo. = $777,600.
I = Pt - Po = 777,600 - 360,000 = $417,600.
To calculate the total amount of interest paid on a 30-year loan, we need to know the loan amount, the interest rate, and the length of the loan. In this case, the loan amount is $450,000, the interest rate is 6%, and the length of the loan is 30 years.
First, let's calculate the down payment. The down payment is 20% of the purchase price, which is 20% of $450,000.
Down payment = 0.20 * $450,000 = $90,000
Next, we need to calculate the loan amount. The loan amount is the purchase price minus the down payment.
Loan amount = $450,000 - $90,000 = $360,000
Now, let's calculate the monthly payment. We can use the formula for calculating the monthly payment on a fixed-rate mortgage:
Monthly payment = Loan amount * (monthly interest rate / (1 - (1 + monthly interest rate) ^ (-number of months)))
The monthly interest rate is the annual interest rate divided by 12, and the number of months is the number of years multiplied by 12.
Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005
Number of months = 30 years * 12 = 360 months
Using these values, we can calculate the monthly payment:
Monthly payment = $360,000 * (0.005 / (1 - (1 + 0.005) ^ (-360))) = $2,157.79
Now, we can calculate the total amount of interest paid over the 30-year loan. The total interest is the monthly payment multiplied by the number of months, minus the loan amount.
Total interest = (Monthly payment * Number of months) - Loan amount
Total interest = ($2,157.79 * 360) - $360,000 = $367,604.40 - $360,000 = $7,604.40
Therefore, the total amount of interest paid on the 30-year loan is $7,604.40.