To calculate the monthly payment on a mortgage loan, we can use a formula called the Amortization Formula. The formula is:
Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
P = Principal amount (loan amount)
r = Monthly interest rate (annual rate divided by 12 and converted to decimal)
n = Total number of payments (30 years multiplied by 12 months)
Let's break down the calculation for your specific mortgage loan:
Principal amount (P) = $100,000 (balance financed after the down payment)
Monthly interest rate (r) = 0.12 / 12 = 0.01
Total number of payments (n) = 30 years * 12 months = 360
Now, let's plug in these values into the formula:
Monthly Payment = $100,000 * 0.01 * (1 + 0.01)^360 / ((1 + 0.01)^360 - 1)
Using a calculator or spreadsheet software, you can compute:
Monthly Payment = $1,029.61 (rounded to the nearest cent)
So, your monthly payment for the mortgage loan will be approximately $1,029.61.
To calculate the total interest paid over 30 years, we can use the formula:
Total Interest = (Monthly Payment * n) - P
Where:
Monthly Payment = $1,029.61 (as calculated above)
n = 360 (as calculated above)
P = Principal amount = $100,000
Now, let's plug in these values into the formula:
Total Interest = ($1,029.61 * 360) - $100,000
Using a calculator or spreadsheet software, you can compute:
Total Interest = $271,456.00
Therefore, over the course of 30 years, you will have paid a total of approximately $271,456.00 in interest.