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 for the home purchase, we can use the formula for a fixed-rate mortgage payment:
M = P × ( 1 + r ) n − 1 r ( 1 + r ) n
Where:
M is the monthly mortgage payment.
P is the principal loan amount.
r is the monthly interest rate.
n is the number of payments (months).
Let's calculate each part:
Down Payment Calculation:
The down payment is 12% of the home price, which is calculated as: Down Payment = 315 , 000 × 0.12 = 37 , 800
Principal Loan Amount ( P ):
The principal P is the remaining amount after the down payment: P = 315 , 000 − 37 , 800 = 277 , 200
Monthly Interest Rate ( r ):
The annual interest rate is 6.8%, so the monthly rate r is: r = 100 × 12 6.8 = 12 0.068 ≈ 0.0056667
Number of Payments ( n ):
This is a 30-year mortgage, so n is calculated as: n = 30 × 12 = 360
Substitute into Mortgage Formula:
Plug these values into the formula to find M :
M = 277 , 200 × ( 1 + 0.0056667 ) 360 − 1 0.0056667 ( 1 + 0.0056667 ) 360
Simplifying the calculations gives: M ≈ 1 , 805.23
Therefore, the monthly mortgage payment is approximately $1,805.23.
