Question

suppose you took a $100,000 15 year fixed-rate mortgage at 4.5% (APR) 3 years ago. Now the market interest rate has dropped to 4%, and you are considering refinance your mortgage.
(1) What was the original monthly payment? (2) Suppose you just made the 36th monthly payments. What is the remaining mortgage balance?
(3) If you refinance with mortgage with another bank and keep the remaining term (that is, 12 years until the mortgage is paid off), what would the new monthly payment be?

Answer 1

Per month ROI = 4.5/12 = 0.375%

EMI = [P*R*(1+R)^N]/[(1+R)^N -1]

EMI = [100000*0.00375*(1+0.00375)^180]/[(1+0.00375)^180-1]

EMI = (375*1.961555)/0.961555

EMI = 765

Remaining balance calculation

FV = {PV(1+r)^n} - P[(1+r)^n - 1/r]

FV = {100000(1+0.00375)^36} - [765(1+0.00375)^36-1]/0.00375

FV = 114424.78 - 765(1.14424 - 1)/0.00375

FV = 114424.78 - 29426.56

FV = 84998.22

Remaining mortgage balance = 84998

New EMI = [84998*0.00333333*(1+0.0033333)^144]/[(1+0.003333)^144 - 1]

= (283.33*1.61478)/(1.61478-1)

= 457.5167/0.61478

New EMI = 744.18