Question

4. Your uncle has had a standard 30-year FRM with a 5% interest rate for 2 years (24 months); the original principal was $200,000. One day he calls you up, very excitedly: “My bank offered to refinance my mortgage to a new 30-year ARM with a 2.5% interest rate. This is awesome – since the interest rate is cut in half, my monthly payment will also be cut in half!”

A. Is the second part of his statement correct? By how much does his payment go down? In addition to showing a calculation, please try to briefly explain intuitively what is going on.

B. How would your answer to part (a) change if your uncle had had his old mortgage for 20 years (240 months) instead?

C. How would your answer to part (a) change if the new mortgage has an initial interest only period?

Answer 1

The second part of his statement is incorrect.

A. For a $200000 FRM, the EMI (PMT) comes to $1069.19. Over 2 years he pays 1069*24=$25660.53. Of this principal amounts to $5940.24. So he refinances 200000-5940.24=194059.76 for 30 years at 2.5% ARM. This emi now comes to $765.18 which is more than half of 1069.19. His payment goes down by 1069.19-765.18=304.01. Intuitively,this is because emi=Decreasing int. each month + Increasing Principal each month to get an equated emi. It is only the interest component which is getting halved, not the principal component.

B. In that case, principal repaid over 2 years would be $6210.09. The emi on refinancing would be 764.11, so payment would go down by 1314.44-764.11=550.32.

C. It would remain the same I suppose as the initial principal repayment foregone would be made up later by a higher emi.