Question

The mortgage on your house is five years old. It required monthly payments of

$1,390​,

had an original term of 30​ years, and had an interest rate of

10%

​(APR). In the intervening five​ years, interest rates have fallen and so you have decided to

refinance—that

​is, you will roll over the outstanding balance into a new mortgage. The new mortgage has a​ 30-year term, requires monthly​ payments, and has an interest rate of

5.625%

​(APR).

a. What monthly repayments will be required with the new​ loan?

b. If you still want to pay off the mortgage in 25​ years, what monthly payment should you make after you​ refinance?

c. Suppose you are willing to continue making monthly payments of

$1,390.

How long will it take you to pay off the mortgage after​ refinancing?d. Suppose you are willing to continue making monthly payments of

$1,390​,

and want to pay off the mortgage in 25 years. How much additional cash can you borrow today as part of the​ refinancing?

​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Answer 1

Part (a)

Loan refinanced = PV of remaining payments from old loan = - PV (Rate, Nper, PMT, FV) = - PV (10%/12, 12 x (30 - 5), 1390, 0) = 152,965.65

Monthly repayments will be required with the new​ loan = PMT (Rate, Nper, PV, FV) = PMT (5.625%/12, 12 x 30, -152965.65, 0) = 880.56

Part (b)

Monthly payment = PMT (Rate, Nper, PV, FV) = PMT (5.625%/12, 12 x 25, -152965.65, 0) = 950.80

Part (c)

It will take months = Nper (Rate, PMT, PV, FV) = Nper (5.625%/12, 1390, -152965.65, 0) = 155.10 months = 12.93
years

Part (d)

PV of all the future payments = - PV (Rate, Nper, PMT, FV) = - PV (5.625%/12, 12 x 25, 1390, 0) = 223,625.56
So, the incremental cash you can borrow today = 223,625.56 - 152,965.65 = 70,659.91