Using the approximation formula, we would fi rst calculate the simple interest rate. The monthly
payments total 12($35) $420, and so the extra $45 can be thought of as interest.I PRT
$45 ($420)R(1)
R 10.71%Plugging this into the approximation formula gives:APR __n 2nr 1
2(12)(0.1071)
_____ 13 19.77%
Whichever rate you use, it may be helpful to have a comparable interest rate in mind when
you are considering a plan of this type. If the rates implied by a rent-to-own plan are com-
parable to the rates you can obtain elsewhere (such as with a credit card), then such a plan
might be reasonable. On the other hand, rent-to-own companies are often accused of charg-
ing rental rates that equate to exorbitant interest rates. If you found, say, that a rent-to-own
plan was equivalent to paying 40% interest, simply buying the item on a credit card might
be a more financially attractive proposition.^7
One significant difference between rent-to-own plans and borrowing of whatever type
is that, until the full rental term has been completed, the renter does not own the item in
question. There is no point in asking a question such as “after 10 months, how much do you
still owe” because you don’t owe anything. While it is appealing to not have any debt for
the item, it also means that if you stop paying on it, it goes back to its owner.
Land contracts are a means of buying real estate that work like rent-to-own plans. They are
most attractive to buyers whose credit is insufficient to qualify for a mortgage; the downside is,
of course, that the buyer does not actually own the property until all payments are made.(^7) Or, you could just save up and pay for it in cash. It’s not as crazy as it sounds. Really.
EXERCISES 10.3
Throughout the exercises for this section, payoff amounts and interest/principal calculations should be found by using the Rule
of 78, unless explicitly stated otherwise.
A. Calculating Installment Plan Payments
- Lennie’s Appliance Megamart has arranged to offer installment plans for major appliance purchases. The plans require
$25 down and 12 monthly payments, and include a 10% carrying charge. If you buy a refrigerator for $850 under this
plan, what will your monthly payments be? - Suppose I buy a lawnmower on an installment plan. The price of the lawnmower is $775.32, the carrying charge is
15%, there is a $50 down payment, and the rest is paid off in monthly installments over the next 2 years. Calculate the
monthly installment payment. - Calculate the monthly payment for a 3-year simple interest loan if the initial balance is $2,750 and the simple interest
rate is 8.25%. - Julian bought a sound system on a simple-interest installment plan. The initial balance for the loan was $835. The plan
requires 18 monthly payments, and the simple interest rate is 12½%. Calculate his monthly payment.
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Exercises 10.3 455