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loan, using the new loan to borrow the amount needed to pay the old one off. In this
example, he could pay off the balance of his 15% loan by borrowing the money he needs
to do that at the more attractive 8% rate. This effectively cuts his interest rate to 8% for the
remaining term of his loan. The following example will illustrate this in more detail:
Example 4.5.4 Suppose Kwame has 12 years remaining on a business loan at 15%,
on which the quarterly payments are $2,531.00. If he refi nances this debt with a new
12-year loan at 8%, what will his new monthly payment be? How much total interest
will he save by doing this?
First we need to determine how much he owes now. There are (12)(4) 48 remaining pay-
ments on his loan, and so
PV PMT a _n (^) | (^) i
PV ($2,531)a __ 48 | (^) .0375
PV ($2,531)(22.11112866)
PV $55,963.27
So this is the amount he needs to pay off the old loan.Borrowing this amount at 8% with
quarterly payments for 12 years would require payments of:
PV PMT a _n (^) | (^) i
$55,963.27 (PMT)a __ 48 | (^) .02
$55,963.27 PMT(30.67311957)
PMT $1,824.51
This results in a savings of $2,531.00 $1,824.51 $706.49 per quarter, or a total of
(48)($706.49) $33,911.52 over the remaining term of the loan. Since refi nancing did not
change the amount of principal he owed, this savings is entirely due to interest.
Obviously, Kwame needs no greater motivation to refinance than the potential to save
nearly $34,000 in interest, and taking advantage of a lower rate is certainly one reason to
replace an existing loan with a new one. Another reason for doing this may be to make
things simpler by combining several smaller loans into a single loan. Doing this is some-
times referred to as consolidating the loans.
Example 4.5.5 Andrea has a car payment of $288.95 a month at 9% with 37 months
remaining, a student loan of $353.08 at 5.4% with 108 months remaining, and a
mortgage payment of $1,104.29 at 7.35% with 19 years remaining.
A fi nance company suggests that she could refi nance her mortgage and consolidate it
with her other loans to lower her monthly payments. They propose that she take out a new
30-year mortgage loan at 7.74%, borrowing enough to pay off all three existing loans.
What would her new monthly payment be?
We fi rst need to calculate the amounts she owed on her existing loans. For the sake of space
we will not show all those calculations here. These amounts can be found as in our previous
examples, by taking the present value of the remaining payments. Doing this, we fi nd that
she owes $9,306 on the car, $30,149 on the student loan, and $135,486 on the house.
To consolidate these, she would need to borrow $9,306 $30,149 $135,486 $174,941
with the new mortgage. Calculating the monthly payment on this present value using 30 years
and 7.75%, we can see that her new payment would be $1,253.30.
This sounds like a pretty good deal. Each month, Andrea is now paying a total of $288.95
$353.08 $1,104.29 $1,746.32. Consolidating these loans will reduce her debt pay-
ments by nearly $500 each month!
There is more to the story, though:
Example 4.5.6 How much, in total, will Andrea save by doing this consolidation?
With the new loan, she will make 360 payments of $1,253.30 each, totaling (360)($1,253.30)
$451,188.
4.5 Amortization Tables 187