Noel purchases a house and gets a 15-year mortgage for $155,000 at 4.75 % APR. In addition to the monthly payment, the lender requires him to pay into an escrow account for the homeowners insurance and property tax. His homeowners insurance is $1100 per year and the property tax is $1500 per year. Determine the monthly payment to the lender that includes the insurance and property tax. Round your answer to the nearest cent.

Answer 1

First, let's calculate Noel's monthly payment for the mortgage.

Using the formula for a fixed-rate mortgage payment:

Monthly payment = P[r(1+r)^n] / [(1+r)^n - 1]

Where:
P = principal amount (loan amount) = $155,000
r = monthly interest rate = 4.75% / 12 = 0.00395833
n = total number of payments = 15 years * 12 months = 180

Plugging in the values:

Monthly payment = $155,000[0.00395833(1+0.00395833)^180] / [(1+0.00395833)^180 - 1]
Monthly payment = $991.57

Next, let's calculate the monthly cost for homeowners insurance and property tax that Noel needs to pay into the escrow account.

Monthly cost of homeowners insurance = $1100 / 12 = $91.67
Monthly cost of property tax = $1500 / 12 = $125

Total monthly escrow payment = Monthly cost of homeowners insurance + Monthly cost of property tax
Total monthly escrow payment = $91.67 + $125 = $216.67

Therefore, Noel's total monthly payment to the lender that includes the insurance and property tax is:

Total monthly payment = Monthly payment for mortgage + Total monthly escrow payment
Total monthly payment = $991.57 + $216.67 = $1208.24

So, Noel's total monthly payment to the lender, including the insurance and property tax, is $1208.24.