You have been living in the house you bought 9 years ago for $400,000. At that time, you took out a loan for 80% of the house at a fixed rate 20-year loan at an annual stated rate of 7.5%. You have just paid off the 108thmonthly payment. Interest rates have meanwhile dropped steadily to 4.5%per year, and you think it is finally time to refinance the remaining balance over the residual loan life. But there is a catch. The fee to refinance your loan is $4,000.

Should you refinance the remaining balance?

How much would you save/lose if you decided to refinance?

The answer is: YES, gain $32,765.35

what I've done:

In case 1 : =PMT(0.075/12,240,320000) = $2,577.90

In case 2:

how much do I have still to pay in month 108 : =PV(0.075/12,132,2577.90) = $231,243.01

Monthly payment between 108 and 240 : =PMT(0.045/12,132,231,243.01) = $2,224.26

Cost in case 1:2,577.90 x 240 = $618,696

cost in case 2: (2,577.90 x 108) + (2,224.26 x 132) + 4,000 = $576,015.52

Difference between the two options :$618,696 -$576,015.52 = $42,680.48