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Da Feng is looking to refinance his home because rates have gone down since he p

ID: 2641830 • Letter: D

Question

Da Feng is looking to refinance his home because rates have gone down since he purchased the house 5 years ago. He started with a 30-year fixed-rate mortgage of $213,000 at an annual rate of 6.70%. He has to make monthly payments. He can now get a 25-year fixed-rate mortgage at an annual rate of 4.10% on the remaining balance of his initial mortgage. This loan also requires monthly payments. In order to re-finance, Da Feng will need to pay closing costs of $2,300. These costs are out of pocket and cannot be rolled into the new mortgage. How much will refinancing save Da Feng?

Explanation / Answer

Monthly payment under old loan: (Using excel formula)

=PMT(0.067/12,360,-213000,0)

= 1374.44

PV of old loan's remaining monthly payment = A*(1-(1+i)^-n)/i

=-PV(0.067/12,300,1374.44,0)

= 199843.70

Monthly payment under new loan : (Using excel formula)

=PMT(0.041/12,300,-199847.7,0)

= 1065.94

Difference in monthly payment of two loans = 1374.44 - 1065.94 = 308.50

PV of difference in monthly payments : (Using excel formula)

=-PV(0.041/12,300,308.5,0)

= 57839.34

Net savings due to refinancing = 57839.34 - 2300

= 55,539.34