ࡱ> uxv@ %bjbjFF ,P,,    FFF8~,|2L~(_aaaaaa$ R"   ___@  _____  _& ԰eF+_d0_##_    # _>,_&$JDb7(bTHE TIME VALUE OF MONEY AND COMPOUNDING It is essential to understand the basics of this, although you dont have to understand the mechanics of it. The reason you want to know this is that it will affect how you invest your moneys and/or pay off debts. Without this knowledge you could be misled, especially when talking about money used over the long term. Ignoring any greed for material things, which would you rather have: a dollar right now or a dollar fifteen years from now. Of course, all other things being equal, youd rather have the dollar now, as it has more value now than 15 years from now. The same is true in financial circles, though it is all tied together with rates of return. Rates of return are stated in terms of percentages. If you invest $10,000 and receive in return for having invested or lent the money $500 a year, you are earning 5% (which, unless stated otherwise, always means per year). If it is in a Certificate of Deposit, it is called interest (interest rate or rate of return in the form of interest). On a stock that is a high dividend stock, it is called dividend return. In an investment, it is called investment rate of return. Since a dollar in the future is different than a dollar right now, there must be some means to evaluate the value of these dollars in some comparable terms. For instance, if one knows one can earn 5% interest on a dollar, then, in investment terms, one would say a $1.00 now is worth the same as a $1.05 in one year, since a $1.00 plus 5% (5% of a $1.00 = $.05) equals that number. Table of equivalent dollars, if the opportunity rate of return is 5%: Refer back to this as you read the explanation: TimeEquivalent to $1.00 nowWhat amount of money at 5%, if invested now would equal a 1.00 received in the futureIf one invests $1 per year at the end of a year, one has, at the end of the periodIndividual dollars investedDifference (interest earned)Now1.001 year1.05.9521.00102 years1.1025.9072.052.0510 years1.6289.61412.58102.5830 years4.3219.23166.443036.44 A dollar now is worth the same as $1.1025 2 years from now. But why, if I earned $.05 on a dollar the first year, did the second year balance not only include an extra $.05 for the extra year that passed, for a total added of $.10? Simply because when we earn interest and that interest is left in the account, it will also earn interest (on the interest). At the beginning of the first year, I lent the bank $1.00 and it paid me $.05. However, at the end of the year, including the first years interest, I left $1.05 with the bank if I didnt withdraw my $.05 interest earned and certainly I deserve interest on all the money I left there, regardless of the source! So, I earned 5% on the extra $.05, or $.0025 (a of a cent), that I invested for the extra year. If I leave money in my account or if I dont pay interest on a loan I have, then I earn that interest on interest, which is called compound interest. Einstein once said compounding is the eighth wonder of the world. So, it pays to know about it and even more to understand it. So, lets discuss the chart of equivalent dollars above. Can I add up $1 now and $1 one year from now and call it $2 now? Or $2 at the end of 1 year? No, because there is a rate of return! You would be adding apples and oranges (i.e. time differentiated dollars that are not the same so they cant be legitimately put into one total and mean anything!). If I took $.952 (95.2 cents) now and invested it for 1 year at 5%, it would equal $1 one year from now, so a $1 now is equal to a $1 now and a $1 one year from now is equal to $.952 now, so the legitimate total of a $1 now plus a dollar a year from now is $1.952 in now dollars. Basically, to add any financial effects up into one amount, one must determine the value in terms of equivalent dollars for the relevant time (i.e. now dollars or ten year from now dollars). The point here is that you should 1. Never accept a total that adds non-equivalent dollars. 2. Never consider alternatives without adjusting for compound interest!!!! See also (following right after this part): An Example Of A Use Of The Idea Of Compounding Helpful Additional Readings: __________________________________________________________________________ AN EXAMPLE OF A USE OF THE IDEA OF COMPOUNDING. Mortgage pre-payment plan If a mortgage pre-payment advocate said to make extra payments on your mortgage, would that be good advice if you could, instead of saving some interest on the mortgage, earn a greater return on another investment over the long term? Absolutely not. But if the advocate said there is no better investment and told you that you could reduce your mortgage through paying extra so that your mortgage was paid off in only 10 years (!) so you wouldnt be burdened with all that extra interest and/or youd beat the lenders at their own business, wouldnt you be tempted? If he told you that you would save $182,262 on a $200,000, 6.5% interest, 30 year mortgage if you merely prepaid an extra $1,000 a month, wouldnt you be impressed? However, if you could have invested that money elsewhere at 7% interest, so youd end up with more money in the long run than if you prepaid the mortgage, would you be as impressed? Or if he told you that the $182,262 saved was actually worth far less in now dollars, would you be as impressed? Hopefully not. Should you pre-pay your mortgage if you have no better use for your money? Yes. It is better to save 6.5% interest rather than let money sit in an account at 4% or 0%, of course. But youve got to look at the other options for using the extra money you have every month. The key discipline here is to have an automatic extra payment (from the extra amount you earn in excess of your expenses) go into the highest return account or highest cost account (e.g. a high interest credit card). Youll be better off in the long term and youll have no extra pressure in not having a mortgage paid off, as youll have extra money set aside to instantly be able to pay it off if you so choose. (See the discussion showing how youd have more assets than debt if you used this strategy under Prepay My Mortgage? The Simplified Version on the Website.) Dont be scared by the mortgage scare its merely playing on your fears. Use a professional advisor who has no stake in selling you a mortgage prepayment program. HELPFUL ADDITIONAL READINGS:  HYPERLINK "http://money.howstuffworks.com/how-to-million-dollars.htm" http://money.howstuffworks.com/how-to-million-dollars.htm  HYPERLINK "http://en.wikipedia.org/wiki/Compound_interest" http://en.wikipedia.org/wiki/Compound_interest The resources at  HYPERLINK "http://www.thelifemanagementalliance.com/Resources/ByArea/FinancialMaterialResources.html" http://www.thelifemanagementalliance.com/Resources/ByArea/FinancialMaterialResources.html (Go to  HYPERLINK "http://www.thelifemanagementalliance.com" www.thelifemanagementalliance.com, Financial/Material and click on Financial/Material Resources or if reading this on that website simply press ctrl button and click on the link, look at Financial Planning books, particularly Quinn)  At  HYPERLINK "http://www.thelifemanagementalliance.com" www.thelifemanagementalliance.com , Financial/Material, Financial Planning, Home  PAGE 2 FILENAME \p C:\Documents and Settings\All Users\Documents\SelfDevelop\Matll\Financial\TimeValueMoney.doc 2007 Keith D. Garrick '()* *+,ruNk89r@$&:@Ba(ǿ˺ǪhWh[+hfofho>hVhuh2Vh1tah2V>* h1ta>*huh 8B>*h 8Bh1taheQhm;hZ,h)phZ,h)p>*hZ,hZ,>*h;(hnI>*h;(h)p>*;()*k l e f G H +,tul$$$$$$$$ $$Ifa$gd1tagd)p$a$gd)p$H%%8,,E,E $$Ifa$gdukd$$Iflֈ8#8)s t0644 laEEE $Ifgd)p $$Ifa$gdu8,,E,E $$Ifa$gdukd$$Iflֈ8#8)s t0644 laEEE $$Ifa$gdu $$Ifa$gdu8,,E,E $$Ifa$gdukdn$$Iflֈ8#8)s t0644 laEEE $$Ifa$gdu $$Ifa$gdu8,,E,E $$Ifa$gdukd%$$Iflֈ8#8)s t0644 la  EEE $$Ifa$gdu $$Ifa$gdu#(8,,E,E $$Ifa$gdukd$$Iflֈ8#8)s t0644 la(.17EEE $$Ifa$gdu $$Ifa$gdu789c8333$3$gd)pkd$$Iflֈ8#8)s t0644 lacd()^_-.^_{|j$$$$$$$$$$$gdMpgd)p()O%&m]^_ch.\_{|ik,0EȻ쳯𯫯hehMDhMDhMD>* hId>*hMphMp>* hMphMp hMp>*hMDhMp>*hThMph;(hchWh+ h__hfofho>@jk{| E!F!!!!!!F"""#$G%H%$$$$$$$$$gdlEgd)p,-hU !!!!!!!!!" " " "D"E"F"G"S"""""~w~ljho>U ho>ho>ho>jho>UhqBhT0JjJhTU hThTjhTUhfofhThMphT>*hWhId hlEhlEjhlE0JUhlEhlE>* hlE>*hhlE>*hlEhchMDhlEhMD>*(""""""""".#0#1#2##########-$$$$$$$$$%%%F%G%H%I%O%P%ؽؽѤvpv hm;0Jjhm;0JUhIdhqBhlE0Jj hlEUjhlEUhlEjhlE0JUhMpjhTUhqBhT0JjhTU hThTjhTUhT ho>ho>ho>jho>UhqBho>0J'P%Q%R%S%`%a%%%%%%%%̾٥ hThThIdhm;hm;CJ aJ hm;hm;0JCJ aJ hm;0JCJaJhm;0JCJaJmHnHujhm;0JCJUaJhm;hm;0JCJaJ!jhm;hm;0JCJUaJjhm;0JUhId0JmHnHu H%%%%%gd)p*&P1:p' 1/ =!"#$%$$If!vh5855)5s55#v8#v#v)#vs#v#v:Vl t65855)5s55$$If!vh5855)5s55#v8#v#v)#vs#v#v:Vl t65855)5s55$$If!vh5855)5s55#v8#v#v)#vs#v#v:Vl t65855)5s55$$If!vh5855)5s55#v8#v#v)#vs#v#v:Vl t65855)5s55$$If!vh5855)5s55#v8#v#v)#vs#v#v:Vl t65855)5s55$$If!vh5855)5s55#v8#v#v)#vs#v#v:Vl t65855)5s55]DyK :http://money.howstuffworks.com/how-to-million-dollars.htmyK thttp://money.howstuffworks.com/how-to-million-dollars.htm1DyK /http://en.wikipedia.org/wiki/Compound_interestyK ^http://en.wikipedia.org/wiki/Compound_interestDyK Zhttp://www.thelifemanagementalliance.com/Resources/ByArea/FinancialMaterialResources.htmlyK http://www.thelifemanagementalliance.com/Resources/ByArea/FinancialMaterialResources.html DyK "www.thelifemanagementalliance.comyK Thttp://www.thelifemanagementalliance.com/ DyK "www.thelifemanagementalliance.comyK Thttp://www.thelifemanagementalliance.com/@@@ NormalCJ_HaJmH sH tH DA@D Default Paragraph FontRi@R  Table Normal4 l4a (k@(No Listj@j 8B Table Grid7:V06U@6 T Hyperlink >*B*ph4@4 m;Header  !4 @"4 m;Footer  !.)@1. m; Page Number>@B> lE Footnote TextCJaJ@&@Q@ lEFootnote ReferenceH*P!()*klefGH+,tul  #(.1789 c d  ( ) ^_-.^_{|jk{|EFFGH00x0x0x0x0x0x000x0x0x0x0x00000x0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0000x0x0x0x0x0x0x00x000x0x0x0x00x0x0x0x0x0x0x0000x00000000000000x0x00x0000x0000000@0x0$@000 "89 c d ( ^_^_{|jk{|EFFG^>00 w^>00^>00^>00^>00^>00^>00^>00^>00^>00^>00^>00^>00^>00^>00^~00\>00^>00\>00\>00\>00\>00\>00\>00\>00\>00\>00T>0 0T>0 00\>0 0\>0 0\>0 0@0^>0 0^>0 0^>0 0^>0 0^>00^>0 000000^~00 04,%("P%%"$%&(7cjH%% !#'% DF1XXXX u!=_X  8BeQV__1tafofMp)pizZ,KnI2VsKW[+BcIdm;TMDlEl  #(.178@..0 ..#@UnknownGz Times New Roman5Symbol3& z Arial"qhkFokFgIn4In4t%243Q H)?BTHE TIME VALUE OF MONEYKeith D. GarrickKeith D. GarrickOh+'0 $0 L X dpxTHE TIME VALUE OF MONEYHE Keith D. Garrick MOeiteitNormal.Keith D. Garrick MO2itMicrosoft Word 10.0@*c@[e@:6eIn՜.+,D՜.+,h$ hp  %The Garrick Financial Alliance, Inc.e4O THE TIME VALUE OF MONEY Title 8@ _PID_HLINKSA8B *http://www.thelifemanagementalliance.com/IZhttp://www.thelifemanagementalliance.com/Resources/ByArea/FinancialMaterialResources.html'U/http://en.wikipedia.org/wiki/Compound_interest:http://money.howstuffworks.com/how-to-million-dollars.htmB*http://www.thelifemanagementalliance.com/  !"#$%&'(*+,-./023456789:;<=>?@ABDEFGHIJLMNOPQRURoot Entry F@*(԰eWData )1Table1#WordDocument,PSummaryInformation(CDocumentSummaryInformation8KCompObjj  FMicrosoft Word Document MSWordDocWord.Document.89qOh+'0 ,8 T ` l xTHE TIME VALUE OF MONEYHE Keith D. Garrick MOeiteitNormal.Keith D. Garrick MO4itMicrosoft Word 10.0@*c@:6e@[e@:6eIn՜.+,D՜.+,h$ hp  %The Garrick Financial Alliance, Inc.e4O THE TIME VALUE OF MONEY Title 8@ _PID_HLINKSA8B *http://www.thelifemanagementalliance.com/IZhttp://www.thelifemanagementalliance.com/Resources/ByArea/FinancialMaterialResources.html'U/http://en.wikipedia.org/wiki/Compound_interest:http://money.howstuffworks.com/how-to-million-dollars.htmB*http://www.thelifemanagementalliance.com/*&P1:p' 1/ =!"#$% 3C:\Documents and Settings\All Users\Documents\SelfDevelop\Matll\Financial\TimeValueMoney.doc P%Q%R%S%`%a%%%%%%%%.P0PPPP̾٥~sb~ h|0JCJaJmHnHu*h|0JmHnHuh| hThThIdhm;hm;CJ aJ hm;hm;0JCJ aJ hm;0JCJaJhm;0JCJaJmHnHujhm;0JCJUaJhm;hm;0JCJaJ!jhm;hm;0JCJUaJjhm;0JUhId0JmHnHuH%%%%%.PPPgd)p@@@ NormalCJ_HaJmH sH tH DA@D Default Paragraph FontRi@R  Table Normal4 l4a (k@(No Listj@j 8B Table Grid7:V06U@6 T Hyperlink >*B*ph4@4 m;Header  !4 @"4 m;Footer  !.)@1. m; Page Number>@B> lE Footnote TextCJaJ@&@Q@ lEFootnote ReferenceH*H@bH | Balloon TextCJOJQJ^JaJP()*klefGH+,tul  #(.1789 c d  ( ) ^_-.^_{|jk{|EFFGH00x0x0x0x0x0x000x0x0x0x0x00000x0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0000x0x0x0x0x0x0x00x000x0x0x0x00x0x0x0x0x0x0x0000x00000000000000x0x00x0000x00000000@0x0$@0080 "89 c d ( ^_^_{|jk{|EFFG^>00 w^>00^>00^>00^>00^>00^>00^>00^>00^>00^>00^>00^>00^>00^>00^~00\>00^>00\>00\>00\>00\>00\>00\>00\>00\>00\>00T>0 0T>0 00\>0 0\>0 0\>0 0@0^>0 0^>0 0^>0 0^>0 0^>00^>0 00000^>00^~00 04,%("P%P"$%&(7cjH%P !#'% DF1XXXX u!=_X 8BeQV__1tafofMp)pizZ,K|nI2VsKW[+BcIdm;TMDlEl  #(.178@..0 ..#hThq  hq * hq *GHPQRa@K@nI@,PJ@.PJ@J@0PzK@|K@PK@UnknownGz Times New Roman5Symbol3& z Arial5& zaTahoma"qhkFokFokFgIn4In4t%243Q H)?BTHE TIME VALUE OF MONEYKeith D. GarrickKeith D. Garrick@ %bjbjFF R,,>> H TTTh8,|h!|L($"RZ$ T555 TT 5@TT5TTp P eu}d 0!$$hhTTTT$T>D,p$  hhD(hhRoot Entry FP e{Data )1Table1#WordDocumentrR  !"#$%]*+,-./023456789:;<=>?@AB^\`abcdefghijklmnopqstwz|ySummaryInformation(DocumentSummaryInformation8CompObjj0Table_$ @ _PID_HLINKSA8B *http://www.thelifemanagementalliance.com/IZhttp://www.thelifemanagementalliance.com/Resources/ByArea/FinancialMaterialResources.html'U/http://en.wikipedia.org/wiki/Compound_interest:http://money.howstuffworks.com/how-to-million-dollars.htmB*http://www.thelifemanagementalliance.com/Oh+'0 ,  FMicrosoft Word Document MSWordDocWord.Document.89q՜.+,D՜.+,h$ hp  %The Garrick Financial Alliance, Inc.e4O THE TIME VALUE OF MONEY Title 88 T ` l xTHE TIME VALUE OF MONEYHE Keith D. Garrick MOeiteitNormal.Keith D. Garrick MO4itMicrosoft Word 10.0@*c@:6e@[e@:6eIn