Question

Yassein is looking to refinance his home because rates have gone down from when he bought his house 10 years ago. He started with a 30-year fixed-rate mortgage of $288,000 at an annual rate of 6.5%. He can now get a 20-year fixed-rate mortgage at an annual rate of 5.5% on the remaining balance of his initial mortgage. (All loans require monthly payments.) In order to re-finance, Yassein will need to pay closing costs of $3,500. These costs are out of pocket and cannot be rolled into the new mortgage. How much will refinancing save Yassein? (i.e. What is the NPV of the refinancing decision?)

Answer 1

For the initial mortgage the final total sum he needed to repay was FV = 288,000*(1 + 6.5%/12)^(12*30) = $2,013,637.82,
his monthly payment was $2,013,637.82/360 = $5,593.44,
so he has repaid $5,593.44*120 = $671,212.61 and he still needs to repay
($2,013,637.82 - $671,212.61) = $1,342,425.21
For the new mortgage the final total sum he needs to repay is FV= 20/30*288,000*(1 + 5.5%/12)^(12*20) = $575,352.11, with $3,500 of additional
costs it will be:
FV = $575,352.11 + $3,500 = $578,852.11
So, NPV = $1,342,425.21 - $578,852.11 = $763,573.10
That's why Yassein will save $763,573.10 with the refinancing of his mortgage.