You purchase a home for $315,000 by making a down payment of 12% and financing the remaining amount with a 30-year mortgage. Your mortgage has an annual percentage rate of 6.8%, compounded monthly. Determine your monthly mortgage payment. Round your answer to the nearest cent. Monthly Mortgage Payment = $
Answer (1)
To determine the monthly mortgage payment, we will use the formula for a fixed-rate mortgage, which is given by:
M = P ⋅ ( 1 + r ) n − 1 r ( 1 + r ) n
Where:
M is the monthly payment
P is the principal amount (loan amount)
r is the monthly interest rate (annual rate divided by 12)
n is the total number of payments (loan term in months)
Step 1: Calculate the Down Payment and Loan Amount
The home is purchased for $315,000 with a 12% down payment:
Down Payment = 0.12 × 315 , 000 = 37 , 800
The remaining principal amount P to be financed:
P = 315 , 000 − 37 , 800 = 277 , 200
Step 2: Determine the Monthly Interest Rate and Total Number of Payments
The annual percentage rate (APR) is 6.8%, compounded monthly, so the monthly interest rate r is:
r = 100 × 12 6.8 = 0.0056667 ≈ 0.005667
The mortgage is for 30 years, so the total number of monthly payments n is:
n = 30 × 12 = 360
Step 3: Calculate the Monthly Mortgage Payment
Substitute these values into the mortgage formula to calculate the monthly payment:
M = 277 , 200 ⋅ ( 1 + 0.005667 ) 360 − 1 0.005667 ( 1 + 0.005667 ) 360
Using a calculator to solve:
M ≈ 1 , 803.06
Therefore, the monthly mortgage payment is approximately $1,803.06.
