After owning his home for 4 years, Braxton wants to refinance his mortgage interest rate from 5% to 3.25%. If his current mortgage payment on his 20-year mortgage is $2,336.72 and he will refinance the unpaid balance for 30 years, what is Braxton's new monthly payment (in dollars)? (Round your answer to the nearest cent.)
Show your work
Step 1: Calculate the remaining balance on the current mortgage.
Using an amortization calculator, we can find the remaining balance on Braxton's current mortgage after 4 years is $368,614.09.
Step 2: Calculate the new monthly payment after refinancing.
Using a mortgage calculator, we can calculate Braxton's new monthly payment with a 3.25% interest rate over a 30-year term would be $1,608.20.
Therefore, Braxton's new monthly payment after refinancing would be $1,608.20.
SHOW YOUR WORK
Step 1: Calculate the remaining balance on the current mortgage.
Using the formula for remaining balance on a mortgage:
Remaining Balance = P*(1 + r)^n - ((1 + r)^n - 1) / r * PMT
Where:
P = Original loan amount = $368,614.09
r = Monthly interest rate = 5%/12 = 0.05/12 = 0.00417
n = Total number of payments = 20 years * 12 months per year = 240 months
PMT = Current monthly payment = $2,336.72
Remaining Balance = $368,614.09 * (1 + 0.00417)^48 - ((1 + 0.00417)^48 - 1) / 0.00417 * $2,336.72
Remaining Balance ≈ $339,603.03
Step 2: Calculate the new monthly payment after refinancing.
Using the formula for calculating a mortgage payment:
New Monthly Payment = P*r*(1 + r)^n / ((1 + r)^n - 1)
Where:
P = Remaining balance after refinancing = $339,603.03
r = Monthly interest rate = 3.25%/12 = 0.0325/12 = 0.00271
n = Total number of payments = 30 years * 12 months per year = 360 months
New Monthly Payment = $339,603.03 * 0.00271 * (1 + 0.00271)^360 / ((1 + 0.00271)^360 - 1)
New Monthly Payment ≈ $1,477.08
Therefore, Braxton's new monthly payment after refinancing would be approximately $1,477.08.