Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Luke and Stacey have 21 years remaining on their mortgage, for which the interes

ID: 3418355 • Letter: L

Question

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?

Explanation / Answer

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

an|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