Answer: To calculate the monthly payment to the lender that includes the insurance and property tax, we need to consider the principal amount of the mortgage, the interest rate, and the escrow amount for insurance and property tax.
Let's break it down step by step:
Step 1: Calculate the monthly interest rate.
The annual percentage rate (APR) is 5.5%, but we need the monthly interest rate. So, divide the APR by 12 (number of months in a year):
Monthly interest rate = 5.5% / 12 = 0.055 / 12 = 0.0045833 (rounded to 7 decimal places)
Step 2: Calculate the number of months for the mortgage.
Since Noel has a 15-year mortgage, the number of months will be 15 years * 12 months/year:
Number of months = 15 years * 12 months/year = 180 months
Step 3: Calculate the monthly payment for the mortgage (excluding escrow).
To calculate the monthly payment for the mortgage, we can use the formula for a fixed-rate mortgage:
Monthly payment (excluding escrow) = P * [r * (1 + r)^n] / [(1 + r)^n - 1]
where:
P = Principal amount of the mortgage = $245,000
r = Monthly interest rate = 0.0045833 (from Step 1)
n = Number of months for the mortgage = 180 (from Step 2)
Monthly payment (excluding escrow) = $245,000 * [0.0045833 * (1 + 0.0045833)^180] / [(1 + 0.0045833)^180 - 1]
Monthly payment (excluding escrow) ≈ $1903.37 (rounded to two decimal places)
Step 4: Calculate the monthly escrow amount for insurance and property tax.
To find the monthly escrow amount, we need to add the annual insurance and property tax amounts and then divide by 12 (number of months):
Monthly escrow amount = (Homeowners insurance + Property tax) / 12
Monthly escrow amount = ($1400 + $2200) / 12
Monthly escrow amount = $360
Step 5: Calculate the total monthly payment to the lender (including escrow).
The total monthly payment to the lender will be the sum of the monthly payment for the mortgage (excluding escrow) and the monthly escrow amount:
Total monthly payment = Monthly payment (excluding escrow) + Monthly escrow amount
Total monthly payment = $1903.37 + $360
Total monthly payment ≈ $2263.37
So, the monthly payment to the lender that includes the insurance and property tax is approximately $2263.37.