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How much money is gained or lost in computer rounding errors in, say, a year? And what happens to this money?
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Mel Earp
Macclesfield, Cheshire, UK
The problem of rounding in financial calculations isn鈥檛, in and of itself, a computer problem. It has been with us almost since the invention of money.
Try to divide 拢1 into seven shares and you end up with a fraction of a penny. When society was cash only, this was difficult indeed. In the distant past, coins were even known to be physically cut into pieces. It could be that this was the origin of the old halfpenny and farthings.
Rounding itself isn鈥檛 an error. The error occurs when rounding is accumulated in one direction, up or down. Accounting practices have long guarded against this, even before computers, when everything was pen and paper. This isn鈥檛 to say that it never happens, but it is unlikely that there is some large pot of rounding money to be had somewhere.
To give an example, suppose I have a debt of 拢100 to pay in 12 monthly instalments. A simple, rounded calculation says that I should pay 拢8.33 per month, but this consistently rounds down and produces an error of 4 pence. Of course, what will happen in practice is that four of the payments will be 拢8.34 (one every three months) or one will be 拢8.37. The calculation to do this properly is only slightly more complicated than a simple division. And if this wasn鈥檛 done properly, no money actually disappears. One of the parties will benefit from the 4 pence 鈥� in the example I describe, that would be me.
Hillary Shaw
Newport, Shropshire, UK
Overall, you might expect rounding errors to cancel out. But in fact, a small amount of 鈥渁ssets鈥� may be destroyed this way. For example, share prices or currency exchange rates will have a long tail distribution of many smaller ones and a few big ones. In other words, there will be a few 100s, more 90s, many more 80s and so forth. And many more .4s, .3s, .2s and .1s would be rounded down than .6s, .7s, and so forth being rounded up.
Accounting practices have long since guarded against rounding errors, even before computers
However, this loss may increase wealth in society. If the distribution of these entitlements becomes less equal as a result of the loss, the wealthy tend to save more, reducing economic activity, whereas poorer people spend all they have, so they keep the economy ticking over. And if the rich gain more wealth, they will probably invest it in real estate, driving up the price of houses for all. Keep rounding share prices down and, overall, the economy gets bigger.
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