Luke and Stacey have 21 years remaining on their mortgage fo

Luke and Stacey have 21 years remaining on their mortgage, for which the interest rate is 8 and 1/2% and the monthly payment is $915.72. They have made all of their payments as scheduled. Mortgage rates have recently conme down quite a bit, and they are thinking about refinancing.

a. How much do they owe today?

b. If the refinance their loan by replacing it with a new, 21-year loan at 5.5%, what will their new payment be?

c. How much would they save by doing this?

d. Suppose that instead of a 21-year loan, Luke and Stacey decided to take out a new, 30-year loan at 6.5%. In that case, what would their new payment be, and how much would they save?

Solution

Luke and Stacey have 21 years remaining on their mortgage, for which the interest rate is 8 and 1/2% and the monthly payment is $915.72. They have made all of their payments as scheduled. Mortgage rates have recently conme down quite a bit, and they are thinking about refinancing.

a. How much do they owe today:

     There are (21)(12) 252 remaining payments

on his loan, and so

PV = PMT a _{n |i}                                    ((8.5/100)/12=0.007)

PV =($915.72)a _{252 |0.007}

PV =($915.72)(118.43)

PV =$112129

b) If the refinance their loan by replacing it with a new, 21-year loan at 5.5%, what will their new payment be

PV = PMT a _{n |i}                                    ((5.5/100)/12=0.004)

PV =($915.72)a _{252 |0.004}

PV =($915.72)(158.84)

PV =$145458

so new paybul is $145458

c. How much would they save by doing this:

             $145458-$112129=$33328

d. Suppose that instead of a 21-year loan, Luke and Stacey decided to take out a new, 30-year loan at 6.5%. In that case, what would their new payment be, and how much would they save.

n=30*12=360.

i=((6.5/100)/12)=0.005

a_n|0.005=161.49

PV = PMT a _{n |i}                                    ((5.5/100)/12=0.004)

PV =($915.72)(161.49)

PV =$147879

so new paybul is $145458