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# "Rule of 78s" calculation

Posted on 2013-01-27
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Does anyone have an example of C# code that does an accurate "Rule of 78s" calculation? I've spent a few hours trying to get this figured out so I can build an amotization table...

I have the table logic built and working. I have spreadsheet values I'm trying to replicate; but I don't understand (and haven't been able to replicate) the fomulas.

Any help here would be greatly appreciated!

Thanks
Payment-Calculator.XLS
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Question by:Miles Thornton
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Expert Comment

ID: 38825182
The "rule of 72" says that if you divide the 72 by the percentage rate, it gives the approximate number of years for the investment to double.

Here is a table showing those values

%      72/%      actual value
1      72      2.047099312
2      36      2.039887344
3      24      2.032794106
4      18      2.025816515
5      14.4      2.018951594
6      12      2.012196472
7      10.3      2.005548375
8      9      1.999004627
9      8      1.992562642
10      7.2      1.98621992
20      3.6      1.927757874
30      2.4      1.876999019
50      1.44      1.792963353

So it's actually pretty close.
The formula for the last column (actual value after 72/P years) is V = (1+P/100)^(72/P)
where P is the percent.
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TommySzalapski earned 2000 total points
ID: 38825189
And here's the actual number of years it would take to double compared to the guess
%      72/%      years
1      72      69.66071689
2      36      35.00278878
3      24      23.44977225
4      18      17.67298769
5      14.4      14.20669908
6      12      11.89566105
7      10.3      10.24476835
8      9      9.006468342
9      8      8.043231727
10      7.2      7.272540897
20      3.6      3.801784017
30      2.4      2.641926796
50      1.44      1.709511291

And here's the formula for the actual number of years to double
=log(2)/log(P/100+1)

Note, that if you replace the 2 with 3, it gives the number of years for the investment to triple. Also note that you can use ln or any other base for log since log(x)/log(y) is the same in any base.
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Author Closing Comment

ID: 38840842
Thank you Tommy Szalapski!
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