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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 one-third 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 one-half 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 12-installment 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 12-month 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 two-thirds of the interest (which would be $150.00) by paying off the loan in one-third 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

 
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