Question

Consider a 15-year, $135,000 mortgage with a rate of 5.75 percent. Four years into the mortgage, rates have fallen to 5 percent. What would be the monthly saving to a homeowner from refinancing the outstanding mortgage balance at the lower rate? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Amount borrowed = $135,000
Annual interest rate = 5.75%
Monthly interest rate = 0.4792%
Period = 15 years or 180 months

Calculation of initial monthly payments:

Let monthly payment be $x

$135,000 = $x/1.004792 + $x/1.004792^2 + … + $x/1.004792^180
$135,000 = $x * (1 - (1/1.004792)^180) / 0.004792
$135,000 = $x * 120.41932
$x = $1,121.08

Monthly payment = $1,121.08

Calculation outstanding balance after 4 years:

Remaining period = 11 years or 132 months

Outstanding balance = $1,121.08/1.004792 + $1,121.08/1.004792^2 + … + $1,121.08/1.004792^132
Outstanding balance = $1,121.08 * (1 - (1/1.004792)^132) / 0.004792
Outstanding balance = $1,121.08 * 97.65405
Outstanding balance = $109,478.00

Calculation of monthly payment after refinancing:

Annual interest rate = 5.00%
Monthly interest rate = 0.4167%
Period = 11 years or 132 months

Let monthly payment be $x

$109,478 = $x/1.004167 + $x/1.004167^2 + … + $x/1.004167^132
$109,478 = $x * (1 - (1/1.004167)^132) / 0.004167
$109,478 = $x * 101.37170
$x = $1,079.97

Monthly payment = $1,079.97

Monthly saving = Initial monthly payment - Monthly payment after refinancing
Monthly saving = $1,121.08 - $1,079.97
Monthly saving = $41.11