THE RULE OF 78's or
What May Happen When You Pay Off A Loan Early
When you borrow from a bank
or other lender, you usually arrange to repay the loan with interest by
a specific date in a number of equal installments.
REPAYING IT EARLY
But after several payments,
you may decide to repay the entire loan earlier than originally scheduled.
You ask the creditor for a payoff figure. You may be disappointed to
learn that the balance due is higher than you anticipated.
Why is it higher? Perhaps
because you thought the interest on the amount borrowed was divided
evenly over the number of payments you agreed to make. Thus, you may
have believed that if you paid the loan in 10 months instead of 30 you
would owe only onethird as much interest.
This is not the way creditors
compute interest, however.
THE RULE OF 78's
Creditors use tables based
on a mathematical formula called "The Rule of 78's"or sometimes
"The Sum of the Digits"to determine how much interest you
have paid at any one point in a loan. This formula takes into consideration
the fact that you pay more interest in the beginning of a loan when
you have the use of more of the money, and you pay less and less interest
as the debt is reduced. Because each payment is the same size, the part
going to pay back the amount borrowed increases as the part representing
interest decreases.
When you decide to pay off
a loan early, the creditor uses The Rule of 78's to determine your "rebate"the
portion of the total interest charge you won't have to pay.
The Rule is recognized as
a practical way to calculate rebates of interest. There are other methods,
but this one is widely used, and it is reflected in a number of state
lending laws.
REMINDERS
The Truth in Lending law
requires that your creditor disclose whether or not you are entitled
to a rebate of the finance charge if the loan is paid off early. Look
for the prepayment terms before you sign a loan agreement. Ask for an
explanation of anything you do not understand.
Making payments before they
are due does not reduce the total interest owed. Only when you pay off
the entire loan early will you save interest. If you have extra money
some months, put it in a savings account to accumulate until you can
pay off the whole loan.
The final payoff figure on
your loan depends primarily on the original time to maturity, but it
may be affected by other factors, such as variances in the payment schedule
or a lag between the date of calculation and the date of payment.
Keep in mind that paying
off a loan in, say, 15 months instead of 30 as originally planned will
not produce a saving of onehalf of the interest.
You may, however be entitled
to a rebate of certain other charges when you prepay a loan, such as
a part of a premium for credit insurance.
HOW TO USE THE RULE OF 78's
The first step is to add
up all the digits for the number of payments scheduled to be made. For
a 12installment loan, add the numbers 1 through 12:
1+2+3+4+5+6+7+8+9+10+11+12
= 78
The answer is "the sum
of the digits" and explains how the rule was named. One might say
the total interest is divided into 78 parts for payment over the term
of the loan.
In the first month, before
making any payments, the borrower has the use of the whole amount borrowed
and therefore pays 12/78's of the total interest in the first payment;
in the second month, he still has the use of 11 parts of the loan and
pays 11/78's of the interest; in the third, 10/78's; and so on down
to the final installment, 1/78.
To add all the numbers
in a series of payments is rather tedious. One can arrive at
the answer quickly by using this formula:
N_{ x (N+1)}
2
N is the number of
payments. In a 12month loan, it looks like this:
12_{ x
(12+1) = 6 x 13 = 78}
2

A LOAN FOR ANN AND DAN
Let us suppose that Ann and
Dan Adams borrow $3,000 from the Second Street State Bank to redecorate
their home. Interest comes to $225, and the total of $3,225 is to be
paid in 15 equal installments of $215.
Using the Rule of 78's, we
can determine how much of each installment represents interest. We add
all the numbers from 1 through 15:
15_{ x (15+1)
= 7.5 x 16 = 120}
2
The first payment will include
15 parts of the total interest, or 15/120's; the second, 14/120's; and
so on.
Notice in the following table
that the interest decreases with each payment and the repayment of the
amount borrowed increases with each payment.
Payment
No. 
Interest 
Reduction
of Debt 
Total
Payment 
1

$
28.13 
$
186.87 
$
215.00 
2

26.25

188.75

215.00

3

24.37

190.36

215.00

4

22.50

192.50

215.00

5

20.63

194.37

215.00

6

18.75

196.25

215.00

7

16.87

198.13

215.00

8

15.00

200.00

215.00

9

13.13

201.87

215.00

10

11.25

203.75

215.00

11

9.37

205.63

215.00

12

7.50

207.50

215.00

13

5.63

209.37

215.00

14

3.75

211.25

215.00

15

1.87

213.13

215.00


$
225.00 
$
3,000.00 
$
3,225.00 
HOW MUCH IS THE REBATE?
Now let's assume Ann and
Dan want to pay off the loan with the fifth payment. We know the total
interest is divided into 120 parts. To find out how many parts will
be rebated, we add up the numbers for the remaining 10 installments
which will be prepaid:
10_{ x (10+1)
= 5 x 11 = 55}
2
Now we know that 55/120's of
the interest will be deducted as a rebate; it amounts to $103.12.
55 _{x $225 = }12375 _{= $103.12}
120
120
We see that Ann and Dan do
not save twothirds of the interest (which would be $150.00) by paying
off the loan in onethird of the time. But the earlier they repay the
loan the higher the portion of interest they do save.
CHECK IT OUT
Perhaps you would like to
try using The Rule of 78's. Here is a problem for you. Assume that Ann
and Dan pay off their loan at Second Street State Bank with the eleventh
payment. How much interest will they save? Remember that the interest
over 15 months is divided into 120 part, and you need to know the number
of payments that will be prepared. Fill in the blanks.
N _{x (N+1) = }?_{x ( ? +1) = ? x ? = ? .}
2
2
Now multiply the rebate fraction by the total amount of interest on the loan:
x $ = $ rebate
Your answers should be as follows:
4 _{x
(4+1) = 2 x 5 = 10}
_{2}
10 _{x $225
= }2250_{ =} _{$18.75}
120
120 
