A quick explanation of the "Rule of 78"

by Clark from Belmont

Occasionally on The Money Show (FM 96.9, WTKK Boston), Rick Shaffer mentions the Rule of 78 in connection with auto loans but declines to explain it in detail because it is too complicated. As an occasional listener and a person who had one of these loans back in 1983, I thought I would make a stab at explaining it...

The standard loan is called "simple interest". You borrow some money and at the end of the period you pay it back plus interest. For longer term loans, you make periodic payments. With some consumer loans, especially with auto loans, you may encounter a different type of loan which mentions the "Rule of 78". It is a different way of deciding how much of each monthly payment is interest and how much is principal.

If you don't terminate the loan early, simple interest loans and Rule of 78 loans will be equivalent. You will pay the same amount and get the interest rate quoted. However, if you pay off the loan early, you will end up paying more interest with a Rule of 78 loan than with the corresponding "simple interest" loan. For that reason, you should not take loans computed on the "Rule of 78".

Here is a simple auto loan with round numbers:

Amount of loan: $10,000
Interest rate: 12% a year (which is 1% a month)
Length of loan: 1 year (12 months)

Simple interest says that after one month has gone by, you have borrowed the $10,000 for 1/12 of a year and you own interest of 12%/12 or 1% which is $100. The rest of your payment goes to decreasing the principal.

The next month you have borrowed $9211.51 for a month and own $92.12 in interest. After paying the interest, the rest of your payment goes to pay off the principal you borrowed.

Figuring out the payments for a simple interest loan is a job for a loan calculator. In our example, it says that the monthly payment is $888.49.

Over the life of the loan you will pay $661.85 in interest.

On the last payment you make, you will have borrowed $879.67 for one month and owe $8.80 in interest. Notice that your final payment is almost all repayment of principal.

If you look at each interest payment, it decreases each month. If you graphed the monthly interest payments, they would form a slight curve.

OK, now let's do the same loan as a Rule of 78 loan:

Amount of loan: $10,000
Total interest due: $661.85 (same as above)
Monthly payment: $888.49 (same as above)
Number of payments: 12
Sum of the integers from 1 to 12: 78 (the magic number)

First month's interest: 12/78 times $661.85
Second month's interest: 11/78 times $661.85
Third month's interest: 10/78 times $661.85
Last month's interest: 1/78 times $661.85

If you were to graph the interest payments, they would form a straight line.

If you were to pay the loan off early, you would have to pay a little extra because the initial payments attribute too much to interest, and too little to principal.

How much does it matter? In our example, the worst it would matter is month 5 where the difference between simple interest and Rule of 78 is $4.01. However, our example was chosen to have round numbers and a 1 year loan.

How much does it matter in a typical auto loan? Consider the following:

Amount of loan: $30,000
Interest rate: 7.3% a year
Length of loan: 4 years (48 months)
Monthly payment: $722.57

If you pay this loan off early, you will always pay more with a Rule Of 78 loan than with a simple interest loan. Between months 7 and 29 you will be paying at least $46 more. Month 17 has you pay $66 more. Is $46 - $66 real money to you?

Here are some related web sites:

Revised: $Date: 2008/11/17 17:34:33 $