Answer to Question #25885 in Finance for shashikant prabhakar

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.