We then can fi nd the rate for this factor by using a table.By the approximation formula:We have to be careful about using the approximation formula. The 10% carrying charge
used to calculate Bill’s payment was not a simple interest rate, which is what that formula
requires. We fi rst must fi gure out the simple interest rate for Bill’s loan.Bill is paying $140 interest for a 9-month loan with $1,400 principle. So the simple interest
rate for this would be:I PRT
$140 ($1,400)R(9/12)
R 13.33%Using this rate in the approximation formula gives us:APR __n 2nr 1
2(9)(0.1333)
____ 10 23.99%
Once again, we see that these two different methods of calculating the rate differ quite a bit,
but still give the same general sense of the actual rates being charged.Installment Plans Today
The sorts of installment plans described in this section, while once commonplace, have
largely disappeared from the American consumer finance landscape. This has happened
for a number of different reasons.
One reason is certainly a result of the Truth in Lending Law and other similar consumer
financial protection laws and regulations. If Tonya is told that her installment plan carries
an 8% simple interest rate, she might not think that is too bad a deal; a 14.68% rate sounds
far less attractive and knowing this might well lead her to consider other options.
Another reason for a move away from these types of plans is mathematical. As we have
seen, calculating annuity factors is a computational challenge, requiring either calculator or
computer tools that have become widely available only in the last few decades, or cumber-
some tables. In contrast, calculating the payments for a simple interest plan requires only a
bit of basic arithmetic. The Rule of 78 offers similar advantages over building an amortiza-
tion table. Because the technology for amortized loans is now widely available, though,
these advantages are no longer so important.
Yet another reason is the increased use of credit cards. Not all that long ago, credit cards
were not as widely accepted or used as they are today. Many readers of this book may be
old enough to remember when grocery stores and most small businesses only grudgingly
accepted credit card payments, if at all, and “pay at the pump” was a novel concept. It
wasn’t all that long ago! But in today’s world it would not be at all unusual for Tonya and
Bill to pay for their purchases on a credit card.
One last reason is the rise of rent-to-own retailers. These businesses offer an enormous
array of consumer goods on plans that allow customers to make monthly rental payments
until, after a certain number of payments have been made, the rented item becomes prop-
erty of the renter. These are not really installment plans, since instead of buying the item
with borrowed money the customer rents the item, but they function in much the same way
and appeal to much the same consumer market as installment plans.
Because of their similarities to installment plans, it can be interesting and worthwhile to
consider them, using the techniques of this section.Example 10.3.8 Suppose that Bob’s Super Rental World offers an LCD television
that would normally sell for $375 on a 12-month rent-to-own contract for $35.00
a month. If this were an installment loan, what would the interest rate be?Using a spreadsheet amortization table with guess and check, we fi nd that the rate works
out to be 21.46%.454 Chapter 10 Consumer Mathematics