Question

Brad decides to purchase a $265,000 house. He wants to finance the entire balance. He has received an APR of 3.8% for a 30 year mortgage. What is Brad's total cost if he takes all 30 years to pay off the house? Round your answer to the nearest hundredth.

Answer 1

To calculate the total cost of Brad's mortgage, you can use the formula for a fixed-rate mortgage payment:

Monthly Payment = P [ r(1 + r)^n ] / [ (1 + r)^n - 1]

Where:
P = principal amount (loan amount) = $265,000
r = monthly interest rate = APR / 12 / 100 = 3.8% / 12 / 100 = 0.00316667
n = total number of payments = 30 years * 12 months/year = 360 months

Plugging in the values:
Monthly Payment = $265,000 [ 0.00316667(1 + 0.00316667)^360 ] / [ (1 + 0.00316667)^360 - 1]

Monthly Payment = $1,231.77

Brad is making payments for 30 years, so the total cost of his mortgage would be:
Total Cost = Monthly Payment * Total Number of Payments
Total Cost = $1,231.77 * 360
Total Cost = $443,237.20

Therefore, the total cost for Brad if he takes all 30 years to pay off the house would be $443,237.20.