- Suppose that I make $100 monthly payments for 24 months on an installment plan where the initial balance was
$2,000.
a. For the Rule of 78, what would my payoff amount be after the 15th payment?
b. For an amortization table, what would my payoff amount be after the 15th payment? - Using the approximation formula, I calculated the APR for a 12-month installment loan to be 28.92%. What would the
rate have come out to be if I had used an amortization table?
10.4 Leasing
Whether it is an individual looking for a car or apartment, or a business looking at office
space or a photocopier, leasing is a widely used alternative to buying property. Some
aspects of the choice between leasing and buying are a matter of personal preference, and
so there really is not much to say about that mathematically. There are, though, interesting
and important mathematical aspects to leasing, and understanding them can give valuable
insights into this option.
Because car leasing is probably the most familiar use of leasing to most readers, we will
initially approach the topic by looking specifically at car leasing. Leasing in other contexts
will be discussed at the end of the section, and explored in some of the exercises as well.Differences between Leasing and Buying
Suppose Jessie is looking for a new car. She has picked out the specific model and features
she wants, but now is left to decide whether to lease the car or to buy it outright, taking out
a loan to finance the purchase. Obviously, one important factor in her decision will be the
monthly payment, but there are other significant differences between the two options.
Leasing is essentially the same as renting the car for a set period of time. If she leases,
she will have the right to drive the car, will have the responsibility for maintaining it and
insuring it, and so on, but she will not actually be the owner of the car. During the term of
the lease, the car belongs to the leasing company, and at the end of the lease, Jessie’s pay-
ments cease and the car must be returned to the leasing company.
Because the car never actually belongs to her and must be ultimately be returned, the
leasing company has the right to place some conditions on how Jessie uses it. The leasing
company will most likely require Jessie to take the car in for all scheduled maintenance,
will require her to repair any damages, and also will limit the total miles that she can put on
the car. Anything about the condition of the car (beyond the results of “normal” use) that
lowers its value will be Jessie’s responsibility to cover when the car is returned.
If Jessie buys the car, she becomes the car’s actual owner. This is true even if she takes
out a loan to buy it. While the lender will most likely have a lien on the car (a provision on
the title that allows the lender to take possession of the car if the loan is not paid as prom-
ised), the car actually is Jessie’s property, albeit with a string attached. At the end of the
loan term, Jessie’s payments cease, but the car remains her property. The lien is then taken
off of the title and she owns it “free and clear.”
Because the car belongs to her, Jessie is not obligated to perform scheduled mainte-
nance. She doesn’t have to change the oil (though she obviously would be foolish not to).
If the paint is scratched or coffee spills stain the upholstery, she may want to clean these up,
but no one will make her to do this. And she is not subject to any limitations on how many
miles she can drive. The car is hers, and while it may be in her best interest to keep it up to
maintain its value, she is not obligated to do so.458 Chapter 10 Consumer Mathematics