Rule of 78
Posted by Christie Malry on February 18, 2010 at 10:34 pm
A few days back I got a call from someone needing some accounting advice. He was trying to draw up some accounts for a client with a lease arrangement. The accounting standard for leases requires that you spread the implicit interest under the lease over the lease term, approximately in proportion to the amount of capital remaining.
Now, this might sound complicated, but it's exactly like a mortgage. If you were to take out a repayment mortgage with a 25 year fixed interest rate, you would be quoted a fixed payment amount that would stay the same for all 300 payments. Your first payment would pay off a tiny portion of the mortgage itself, and the rest would cover interest. Your next payment would pay off a tiny amount more of the mortage and a slightly smaller amount of interest than before. And so on... until your final few payments, which would be mostly mortgage and almost no interest.
In the days of fast computers and spreadsheets, working this sort of thing out is trivial. But it wasn't always like this. So that's why some bright spark invented what is now known as the Rule of 78. It works as follows:
- Imagine a year's worth of payments.
- Number the first month 12, the second 11, the third 10, etc.
- Now you divide each month by 78. Why 78? Because 78 is the sum of each of the integers from 1 through 12.
- The resulting fractions are the amount of interest you repay with each monthly payment.
It's worth pointing out that the Rule of 78 is better for short loans than for longer ones. But it's quite handy if you're stuck on a desert island and are in need of drawing up a quick loan agreement. And there are those who think it would be a rather good name for a punk band.
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