A 40 year fixed mortgage is a home loan with a repayment term of 40 years and an interest rate that remains constant throughout the life of the loan. This type of mortgage offers lower monthly payments compared to shorter-term loans, but results in more total interest paid over the life of the loan.
Formula for Monthly Mortgage Payment
The formula for calculating the monthly principal and interest payment of a 40 year fixed mortgage is:
\[P = L[\frac{c(1+c)^n}{(1+c)^n-1}]\]
Where:
P = Monthly Principal & Interest Payment
L = Loan Amount
c = Monthly Interest Rate (Annual Rate / 12)
n = Total Number of Months (480 for a 40 year mortgage)
Calculation Steps
Convert the annual interest rate to a monthly rate by dividing by 12.
Use the formula above to calculate the monthly principal and interest payment.
Add monthly property tax and insurance (if applicable) to get the total monthly payment.
Example
Let's consider a 40 year fixed mortgage with the following details:
Loan Amount: $300,000
Annual Interest Rate: 4%
Annual Property Tax: $3,600
Annual Home Insurance: $1,200
Calculation:
Monthly interest rate: 4% / 12 = 0.3333%
Monthly principal & interest: $1,193.54
Monthly property tax: $3,600 / 12 = $300
Monthly home insurance: $1,200 / 12 = $100
Total monthly payment: $1,193.54 + $300 + $100 = $1,593.54
Green: Principal & Interest ($1,193.54), Blue: Property Tax ($300), Red: Home Insurance ($100)
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