Question

Three years ago, you bought a house. You took out a $350,000.00 mortgage at 4.75% for 30 years. Now that interest rates have fallen (beginning of year 4 of your current mortgage), you are considering refinancing your existing loan with a new 30 year loan. Your new loan must pay off the remaining balance of your old loan plus pay for all of the fees, associated with the new loan. In addition to all of the standard fees, you choose to spend 1% in points to buy down your interest rate to 2.5%.

All refinancing fees $5,000

Points 1%

How long will it take to payback the cost of refinancing your mortgage? What are the total savings over the life of the loan?

Answer 1

PMT under original loan = PMT (Rate, Nper, PV, FV) = PMT (4.75%/12, 12 x 30, -350000, 0) = 1,825.77

Loan outstanding at the beginning of year 4 = -PV (Rate, Nper, PMT, FV) = - PV (4.75%/12, 12 x (30 - 3),1825.77, 0)=  332,998.40

Loan to be taken out now =  (Current outstanding + All refinancing fees) / (1 - Points) = (332,998.40 + 5,000) / (1 - 1%) =  341,412.53

Hence, PMT under new loan = PMT (Rate, Nper, PV, FV) = PMT (2.5%/12, 12 x 30, -341412.53, 0) = 1,348.99

Hence, monthly saving = PMT under old loan - PMT under new loan = 1,825.77 - 1,348.99 =  476.77

Total cost of refinancing = 1% point + all refinancing fees = 1% x 341,412.53 + 5,000 =  8,414.13

Hence, months it will take to payback the cost of refinancing your mortgage = total cost of refinancing / monthly savings = 8,414.13 / 476.77 =  17.65 months (say 1.5 years).

Total savings over the life of the loan = Old PMT x remaining NPER - New PMT x New NPER =  1,825.77 x (30 - 3) x 12 - 1,348.99 x 12 x 30 = $ 105,910.87