CNBC.com reported mortgage applications increased 9.9% due to a decrease in the rate on 30-year fixed-rate mortgages. Joe Sisneros wants to purchase a vacation home for $320,000 with 20% down. Calculate his monthly payment for a 30-year mortgage at 6.0%. Calculate total interest.
Question
CNBC.com reported mortgage applications increased 9.9% due to a decrease in the rate on 30-year fixed-rate mortgages. Joe Sisneros wants to purchase a vacation home for $320,000 with 20% down. Calculate his monthly payment for a 30-year mortgage at 6.0%. Calculate total interest.
Solution
To calculate Joe's monthly payment for a 30-year mortgage at 6.0%, we first need to determine the amount of the loan. Since he is putting 20% down on a $320,000 home, the amount of the loan is 80% of the home price.
Step 1: Calculate the loan amount Down payment = 20% of 320,000 * 0.20 = 320,000 - 256,000
Step 2: Calculate the monthly interest rate The annual interest rate is 6.0%, so the monthly interest rate is 6.0% / 12 months = 0.5% = 0.005 (in decimal form)
Step 3: Calculate the number of payments The loan term is 30 years, so the number of monthly payments is 30 years * 12 months/year = 360 payments
Step 4: Calculate the monthly payment We can use the formula for the monthly payment on a fixed-rate mortgage, which is:
M = P[r(1+r)^n]/[(1+r)^n – 1]
where: M is your monthly payment. P is the principal loan amount. r is your monthly interest rate. n is number of payments (the number of months you will be paying the loan)
So, M = 1,536.82
So, Joe's monthly payment for a 30-year mortgage at 6.0% would be approximately $1,536.82.
Step 5: Calculate total interest Total amount paid = Monthly payment * Number of payments = 553,255.20 Total interest = Total amount paid - Loan amount = 256,000 = $297,255.20
So, Joe would pay approximately $297,255.20 in interest over the life of the loan.
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