460 Chapter 10 Consumer Mathematics
The following example will illustrate:Example 10.4.2 Using the information provided so far about Jessie’s car lease,
determine the appropriate monthly lease payment. Assume an 8.4% interest rate.Payment on Loss: The loss in value is $5,820. The monthly payment on this would be:PV PMT a _n (^) |i
$5,820 PMT a __ 24 | (^) 0.007
$5,820 PMT(22.02160857)
PMT $264.29
Interest on Residual: The residual value is $14,055. The monthly interest on this would
come to:
I PRT
I ($14,055)(0.084)(1/12)
I $98.39
The lease payment would then be the sum of these two values:
Lease payment $264.29 $98.39 $362.68
Note that, of the two components that go into the total lease payment, the payment on loss
is the larger one, even though the loss in value itself is small in comparison to the residual
value. This is because the payment on loss must include both principal and interest, instead
of just interest. This can lead to some surprising results, though, as the following example
will illustrate.
Example 10.4.3 Ajay is considering taking out a 2-year lease on a new car. The
total price of the car would be $23,850, and the residual value is $18,350. He owns a
car now, worth $4,800, which he will trade in when he gets his new vehicle. Calculate
his lease payment, assuming an 8.7% interest rate.
The idea here is pretty much the same as in Example 10.4.2, except for the existence of the
trade-in. When he leases the car, he “borrows” $23,850. But his trade-in is worth $4,800,
so in fact this is immediately reduced to $23,850 $4,800 $19,050. The loss in value,
then, is only $19,050 $18,350 $700! Proceeding with our calculation:
Payment on loss:
PV PMT a _n (^) |i
$700 PMT a __ 24 | (^) 0.00725
$700 PMT(21.95523688)
PMT $31.88
Interest on residual:
I PRT
I ($18,350)(0.087)(1/12)
I $133.04
Total payment:
Payment $31.88 $133.04 $164.92
By comparison, if Ajay had bought the car and financed it with a 5-year loan at the same
8.7% rate, his monthly payment would have been $392.68. The trade-in dramatically cut
the loss in value, and since that makes up the more significant component of the lease pay-
ment, the lease payment is shockingly low for a new car costing well over $20,000. If Ajay
didn’t have a car to trade in, he could have still got to this low monthly lease payment by
putting $4,800 down (assuming, of course, that he can come up with that much money for
his lease down payment). Sometimes you may see lease payments advertised that just look
too good to be true; the payments may well be for real, but require a significant down pay-
ment, either in the form of cash or a trade-in.