Path: csiph.com!feeder.erje.net!2.us.feeder.erje.net!feeder.usenetexpress.com!feeder1.iad1.usenetexpress.com!border1.nntp.dca1.giganews.com!nntp.giganews.com!buffer1.nntp.dca1.giganews.com!nntp.earthlink.com!news.earthlink.com.POSTED!not-for-mail NNTP-Posting-Date: Mon, 19 Jun 2017 22:00:45 -0500 Message-ID: <5948900A.CCE@ix.netcom.com> Date: Mon, 19 Jun 2017 20:01:30 -0700 From: The Starmaker Reply-To: starmaker@ix.netcom.com X-Mailer: Mozilla 3.04Gold (WinNT; U) MIME-Version: 1.0 Newsgroups: sci.math,sci.physics,sci.physics.relativity,rec.arts.sf.written,alt.astronomy, Subject: Re: The Rule Of 72 References: <59441500.660A@ix.netcom.com> <59441500.660A@ix.netcom.com> <59441500.660A@ix.netcom.com> <59441500.660A@ix.netcom.com> <59441500.660A@ix.netcom.com> <59441500.660A@ix.netcom.com> <59441500.660A@ix.netcom.com> <59480DFB.46CB@ix.netcom.com> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Antivirus: Avast (VPS 170619-2, 06/19/2017), Outbound message X-Antivirus-Status: Clean Lines: 82 X-Usenet-Provider: http://www.giganews.com NNTP-Posting-Host: 108.219.229.47 X-Trace: sv3-pmDrmSYO7BW+hNVTv9Q/gpdQDcH8Lud+/SwNgD8C94Jnywhk+kN3oXxiM/Uwyh0Riz0Icx54QQvD5+E!CcSVyKC3GKj8bZ3H2bjQSdtgn3YOeo6GFiGbrnP0dYeBlAOlFPk7u/fbkLo+mh1av5pI+0Jgu+M1!PBWlw3eJEQ== X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.40 X-Original-Bytes: 4275 Xref: csiph.com sci.math:377437 sci.physics:637033 sci.physics.relativity:423056 rec.arts.sf.written:473607 alt.astronomy:291580 The Starmaker wrote: > > jmfbahciv wrote: > > > > Jack Fearnley wrote: > > > On Sun, 18 Jun 2017 13:21:35 +0000, jmfbahciv wrote: > > > > > > > > >>> > > >> But it's a fast way to estimate the time to double the original amount > > >> when the interest or dividends are reinvested. > > >> > > >> IIRC, divide 72 by the percentage. That will give the number of year to > > >> double the original amount. > > >> > > >> /BAH > > > > > > The exact doubling time is log(2)/log(1+r/100). > > > If we expand log in a Taylor series and take only the first term > > > we get the approximate doubling time as 100*log(2)/r. > > > That is 69.315/r. > > > > > > So why don't we use a rule of 69 or a rule of 70? > > > > > > It turns out that, in the range 1% to 10% and rounded to whole years, 72 > > > is more accurate than 69.315. > > > > > > I found this quite surprising. > > > > There are a lot of accounting tricks having to with 9s. I suppose people > > aren't being taught these rules since most accounting is done by computer > > rather than "by hand". ISTM there was a book published which described > > these "9" tricks. I always meant to figure out proofs for them but > > life got in the way :-). When you first encounter these tricks of the > > trade, you think it's magic. > > > > /BAH > > You mean like the value someone came up with the speed of light accounting trick: > > 299,792,458 meters per second > > 299 > > it ends like a 99.9 percent ( how these guys think when they are unsure) > > 299...just short of 300 > > keeping it under the true value of over 300,000,000. > > Then I notice other "9" patterns... > > 299,792,458 > > 792 > > 7+2=9 > > 458 > > 4+5=9 > > 299,792,458 meters per second is an accounting trick, isn't it???? Okay...going a step further on the "9" accounting trick.. How many nines are there in 299,792,458? There are three numbered "9"'s There are 4+5=9 and 7+2=9 2+7=9 So that totals 3 more "9"s Then you have nine digits - 299,792,458 299,792,458 meters per second is an accounting trick, isn't it???? What is the speed of light? 99999999999999999999999998 good thing i'm not good at arithmetic...