Rule of 78

Posted by Professor Cram in Consumer Credit and Banking

Rule of 78

The Rule of 78 is a method of allocating interest charges for the life of a loan to the periods within the loan. It was developed as a simple (but inaccurate) method for calculating interest refunds in case of early repayment of a loan. The existence of financial calculators and electronic spreadsheets with financial calculation capability renders this an archaic practice. (See Compound Interest Made Simple for an easier way to find compound interest.)

The Rule of 78 methodology also allocates a slower payoff of the loan and higher interest charges for early payoff than using outstanding balance. This method was outlawed in the U.S. in 1992 for loans longer than 5 years. Use on loans for less than 61 months is subject to state laws.

Under the Rule of 78 method, interest is calculated for the life of the loan and then allocated to each month by proportion using reverse sum of the digits methodology. You start by adding up the numbers of months for the note. For example, in a 12 month loan, counting month 1, plus month 2, and so forth through month 12 is:

    1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

This totals 78, and hence the name, rule of 78s.

The simple interest total for the loan life (as given by the formula: Interest = Rate x Time x Principal) is divided by the sum of the digits (78 in this example) and applied in reverse proportion across the life of the loan. Thus, 12/78 of the interest applies to the first month, 11/78 to the second month, and so forth down to 1/78th at the end of the 12th month.

Example of Rule of 78

Let's look at the example of a $20,000 loan at 5% interest for 2 years. Under the Rule of 78 method, we first add up the months for the note:

  • 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 = 300

Now, we calculate the simple interest total for the life of this loan:

  • Interest = Rate x Time x Principal
  • Interest = 5% x 2 years x $20,000
  • Interest = $2,000

Finally, we divide the interest total by the sum of the digits (300) and apply in reverse proportion:

  • Month #1: $2,000 x (24/300) = $160
  • Month #2: $2,000 x (23/300) = $153
  • Month #3: $2,000 x (22/300) = $147
  • Month #4: $2,000 x (21/300) = $140
  • ……..
  • Month #22: $2,000 x (3/300) = $20
  • Month #23: $2,000 x (2/300) = $13
  • Month #24: $2,000 x (1/300) = $7

As you can see, the amount of interest in the Rule of 78 is higher in the beginning and reduces over the life of the loan.

A point for multiple choice exams - the rule of 78 does NOT refer to the year the rule was adopted or banned.

A last important lesson: the Rule of 78 doesn't need to have the number 78 in it!



15 Responses to “Rule of 78”

  1. Usetim itoro akpan says:

    If i ask to give out the raw of mathematic is it be correct of dis?

  2. Natasha says:

    Good Day Mate, I am commenting from Warragul-Drouin Australia. We have had a lot of wind squalls lately and I’ve only just been able to log onto the internet Thanks for the useful blog. It helped me a lot with my TAFE internet research research. God Bless the internet !

  3. Wanda Strickfaden says:

    Nice post. I learn something new and challenging on sites I stumbleupon everyday.
    It’s always exciting to read articles from other authors and practice something from other websites.

  4. white jacobs & associates says:

    Have you ever considered the other perspectives? Seems a little narrow here

  5. software says:

    Thanks for sharing your thoughts on 78. Regards

  6. Farming Simulator 14 Hack says:

    Hi there, just became alert to your blog through Google, and found that it’s really informative.
    I am going to watch out for brussels. I will be grateful if you continue this in future.
    A lot of people will be benefited from your writing.


  7. Lucius Livecchi says:

    Thanks for your marvelous posting! I truly enjoyed reading it, you’re a great author.I will make sure to bookmark your blog and definitely will come back sometime soon. I want to encourage continue your great writing, have a nice weekend!

  8. Chloe Lally says:

    This web site doesn’t show up appropriately on my android – you might want to try and repair that

  9. Lana Bedonie says:

    Admiring the commitment you put into your blog and detailed information you present. It’s great to come across a blog every once in a while that isn’t the same old rehashed information. Great read! I’ve saved your site and I’m adding your RSS feeds to my Google account.

  10. Randall Fabre says:

    I truly enjoy examining on this website , it has wonderful content.

  11. Jocelyn says:

    Hi just want to know because I have an existing loan with Toyota Financial Services my Prinicpal Loan is 609,600.00 my monthly installment is 14981.00 payable for 60 months.

    The toyota financial services use the rule of 78 but the loanable amount is 898860.00 the principal amount 609,600.00 plus the interest of 289,260.00 total is 898,860.00

    The unit was declared total loss and I am still paying my monthly amortization because the Insurance company is still in process.

    So I contact the toyota finanical services informing me that 25 months of paying my balance is 534,335.00 .

    As of my computatiion using the rule of 78 , as of paying 25th months the balance should be 424,753.69

    May I know the real blance as of Octber 2015.

  12. Candra Eckels says:

    Excellent blog you have here but I was wanting to know if you knew of any discussion boards that cover the same topics discussed in this article? I’d really like to be a part of group where I can get feed-back from other experienced individuals that share the same interest. If you have any recommendations, please let me know. Thanks a lot!

  13. Cheap Private Proxies says:

    I’m really loving the theme/design of your website. Do you ever run into any browser compatibility issues? A small number of my blog audience have complained about my blog not working correctly in Explorer but looks great in Opera. Do you have any tips to help fix this issue?

  14. agen sabung ayam says:

    Great – I should certainly pronounce, impressed with your web site. I had no trouble navigating through all tabs and related information ended up being truly easy to do to access. I recently found what I hoped for before you know it at all. Reasonably unusual. Is likely to appreciate it for those who add forums or anything, web site theme . a tones way for your customer to communicate. Nice task..

  15. agen sabung ayam says:

    I’m usually to blogging and i actually respect your content. The article has really peaks my interest. I am going to bookmark your site and hold checking for brand new information.

Leave a Reply

Get More Help!

Click one of these links to get more help from another Cramlet in this same chapter: