To calculate the monthly payment for a home mortgage, we can use the formula for amortizing loans. The formula is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate (APR / number of months in a year)
n = Number of total payments (number of years * 12)
Let's calculate the monthly payment for a home mortgage of $125,000 at a fixed APR of 9% for 30 years:
Step 1: Convert APR to monthly interest rate
r = 0.09 / 12 = 0.0075
Step 2: Calculate the number of total payments
n = 30 * 12 = 360
Step 3: Plug the values into the formula
M = 125,000 * (0.0075 * (1 + 0.0075)^360) / ((1 + 0.0075)^360 - 1)
After solving this equation, the monthly payment (M) comes out to be approximately $1,004.62.
To determine the total amount paid over the term of the loan, we need to multiply the monthly payment by the number of total payments:
Total amount paid = Monthly payment * Number of total payments
Total amount paid = $1,004.62 * 360
Total amount paid = $361,657.20
Thus, the total payment over the term of the loan is $361,657.20.
To calculate the percentage of the total payment that goes towards the principal and interest, we need to consider the amortization schedule of the loan. However, for a general estimate, we can assume that in the early years of the loan, a higher percentage goes towards interest, while towards the later years, a higher percentage goes towards the principal.
As a rough estimate:
- Around 70-80% of the total payment may go towards interest in the early years.
- Around 20-30% of the total payment may go towards the principal in the early years.
- These percentages gradually reverse over time until the final payments consist mostly of principal.
Please keep in mind that these estimates may vary depending on the specific terms of the loan and actual interest calculations.