You borrow $185,000 to buy a house. The mortgage rate is 6.5 percent and the loan period is 32 years. Payments are made monthly. If you pay the mortgage according to the loan agreement, how much total interest will you pay?
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To find the total interest you will pay on your mortgage, you need to use the formula for calculating mortgage payments. The formula is:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P = monthly mortgage payment
r = monthly interest rate (annual interest rate divided by 12)
A = loan amount
n = total number of payments
First, let's calculate the variables needed for the formula:
r = 6.5% / 100 / 12 = 0.0054167 (monthly interest rate)
A = $185,000 (loan amount)
n = 32 years * 12 months = 384 (total number of payments)
Now, plug in the values into the formula to calculate the monthly mortgage payment (P):
P = (0.0054167 * 185000) / (1 - (1 + 0.0054167)^(-384))
P ≈ $1,166.96
Next, multiply the monthly mortgage payment (P) by the total number of payments (n) to find the total amount paid over the loan period:
Total amount paid = P * n
Total amount paid = $1,166.96 * 384
Total amount paid ≈ $448,547.84
Lastly, subtract the loan amount (A) from the total amount paid to calculate the total interest paid:
Total interest paid = Total amount paid - A
Total interest paid = $448,547.84 - $185,000
Total interest paid ≈ $263,547.84
So, the total interest you will pay over the 32-year loan period is approximately $263,547.84.