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	<title>big-oh notation - Tan Quach &#187; rounding errors</title>
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	<description>The secret to happiness is low expectations.</description>
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		<title>How to Make Millions off Rounding Errors</title>
		<link>http://www.tanquach.com/blog/2010/02/03/how-to-make-millions-off-rounding-errors/</link>
		<comments>http://www.tanquach.com/blog/2010/02/03/how-to-make-millions-off-rounding-errors/#comments</comments>
		<pubDate>Wed, 03 Feb 2010 22:07:58 +0000</pubDate>
		<dc:creator>tan</dc:creator>
				<category><![CDATA[General]]></category>
		<category><![CDATA[bell]]></category>
		<category><![CDATA[rounding errors]]></category>

		<guid isPermaLink="false">http://www.tanquach.com/blog/?p=170</guid>
		<description><![CDATA[Ahh, tax season. The most wonderful time of the year. I recently discovered while going through my past year&#8217;s expenses, that Bell Mobility (my cell phone carrier) has been over-charging me on taxes every month. Well, 11/12 months, actually. Once did I see a rounding error in my favour.
This was odd, but not entirely surprising. [...]]]></description>
			<content:encoded><![CDATA[<p>Ahh, tax season. The most wonderful time of the year. I recently discovered while going through my past year&#8217;s expenses, that Bell Mobility (my cell phone carrier) has been over-charging me on taxes every month. Well, 11/12 months, actually. Once did I see a rounding error in my favour.</p>
<p>This was odd, but not entirely surprising. Bell Canada obviously has legacy software, and as a practitioner I can see how these bugs can get in. But did other people experience this? Did anyone else even care?</p>
<p>On my bill, I found that sometimes the taxes were being rounded up instead of down and other times, just completely wrong as it was off by at most 6 cents sometimes.</p>
<p>When you think about it, 6 cents is not a lot, nor is it worth 20 minutes on the phone with a Bell CSR who doesn&#8217;t stop laughing at you and making smarmy comments about writing you a cheque for $0.06.</p>
<p>But 2 cents, 6 cents, whatever, every month adds up. It adds up to $1.51 over a year in fact. And with 7-8 million customers who don&#8217;t notice, that&#8217;s a lot of revenue for Ma Bell.</p>
<p>So, I went immediately to Google to complain and sure enough there were other people experiencing the same problem but didn&#8217;t feel the need to fight it.</p>
<p>After talking to the CSR, it was revealed that this was in fact, <em>by design</em>. This is part of the billing software because they charge tax on every line item on your phone bill. If the line item was $0.35, they&#8217;d round up $0.0455 cents to an even $0.05.</p>
<p>On my last phone bill, there was over 200 line items, each one being either rounded up or down after having taxes applied. The end result? The sum total was off by $0.04 cents.</p>
<p>So how would you convince Bell to stop this madness? In high school, they taught us about significant digits and how you should keep track of significant digits until at the end before rounding the value. Clearly, whoever programmed this billing system is accumulating fractions of pennies in an off-shore bank account somewhere.</p>
<p>If you&#8217;re a small business or incorporated, you can claim back the GST that you paid. This means there is an opportunity here to actually make money! The key is to maximize the number of times Bell rounds down on each line item. That means making quick phone calls that last less than a minute repeatedly. If you do this a few thousand times, you might be able to make $0.50! Just imagine the money piling in!</p>
<p>I&#8217;ve made a quick chart of how this works out. Hopefully it explains things a lot clearer than I can explain.</p>
<div class="wp-caption aligncenter" style="width: 514px"><img title="Making Money off Rounding Errors" src="http://images.cheezburger.com/completestore/2010/2/3/129097076518074085.png" alt="Now all you need is a (money) laundramat." width="504" height="497" /><p class="wp-caption-text">Now all you need is a (money) Laundromat.</p></div>
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