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
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