Comments on: Commutative Law of Multiplication http://thefinancebuff.com/commutative-law-of-multiplication.html like a friend telling you about money ... Fri, 10 Feb 2012 17:31:35 +0000 hourly 1 http://wordpress.org/?v=3.1.2 By: bill http://thefinancebuff.com/commutative-law-of-multiplication.html#comment-7567 bill Tue, 27 Dec 2011 18:31:35 +0000 http://blog.thefinancebuff.com/?p=126#comment-7567 but i think the author forgot about one fact (it is almost fact, if it is not 100% right), ie, $ is getting depreciated. so paying a lump-sum tax bill 30 years from now is better than paying NOW. in this way, even if tax rate are the same 30 years from now, i would argue that traditional is better than roth (with time value of money in consideration). but i think the author forgot about one fact (it is almost fact, if it is not 100% right), ie, $ is getting depreciated. so paying a lump-sum tax bill 30 years from now is better than paying NOW. in this way, even if tax rate are the same 30 years from now, i would argue that traditional is better than roth (with time value of money in consideration).

]]> By: Tom http://thefinancebuff.com/commutative-law-of-multiplication.html#comment-4713 Tom Thu, 16 Sep 2010 17:50:16 +0000 http://blog.thefinancebuff.com/?p=126#comment-4713 Nice post, agree that the simple dollar is often, well, too simple in its analysis. However, isn't your math wrong? What I mean is, the point you make is correct, you either pay tax upfront or on the back end, but you shouldn't use two variables for taxation. Saying n * (1 – t1) = (1 – t0) * n is like saying n*(1-x)= (1-y)*n, which is not an example of the commutative property, its an equation with three variables. Nice post, agree that the simple dollar is often, well, too simple in its analysis.

However, isn’t your math wrong? What I mean is, the point you make is correct, you either pay tax upfront or on the back end, but you shouldn’t use two variables for taxation.

Saying n * (1 – t1) = (1 – t0) * n
is like saying n*(1-x)= (1-y)*n, which is not an example of the commutative property, its an equation with three variables.

]]> By: Fred http://thefinancebuff.com/commutative-law-of-multiplication.html#comment-3921 Fred Sun, 02 May 2010 04:25:43 +0000 http://blog.thefinancebuff.com/?p=126#comment-3921 The common misconception is that the Roth option is better because "your earnings grow tax-free." Looking closely at this claim: If the future value of your investment is FV, and the present value is PV, then FV=PV(1+i)^y, where i is the interest rate per period and y is the number of periods the investment accumulates interest. For a traditional 401k, taxes are applied after interest has compounded, i.e. FV=(PV(1+i)^y)(1-t0). With the Roth option, taxes are applied to the present value, before interest accumulates, i.e. FV=(PV(1-t1))(1+i)^y. Because of the commutative property (not "law") of multiplication, and assuming t1=t0, the FV is the same for both options. So although it seems that your earnings would grow tax-free for the Roth option, in fact, it's more like the government taxes your earnings before you earn them. The common misconception is that the Roth option is better because “your earnings grow tax-free.” Looking closely at this claim:

If the future value of your investment is FV, and the present value is PV, then FV=PV(1+i)^y, where i is the interest rate per period and y is the number of periods the investment accumulates interest. For a traditional 401k, taxes are applied after interest has compounded, i.e. FV=(PV(1+i)^y)(1-t0). With the Roth option, taxes are applied to the present value, before interest accumulates, i.e. FV=(PV(1-t1))(1+i)^y. Because of the commutative property (not “law”) of multiplication, and assuming t1=t0, the FV is the same for both options. So although it seems that your earnings would grow tax-free for the Roth option, in fact, it’s more like the government taxes your earnings before you earn them.

]]> By: TFB http://thefinancebuff.com/commutative-law-of-multiplication.html#comment-554 TFB Mon, 31 Mar 2008 22:16:00 +0000 http://blog.thefinancebuff.com/?p=126#comment-554 Kyle - I hear you. The contribution limit is a problem, but only if you hit the limit. If contributing to a Roth IRA means contributing more, you can also increase the contribution to the traditional 401k instead. According to this <a HREF="https://institutional.vanguard.com/VGApp/iip/site/institutional/researchcommentary/article?File=CRR_HowAmericaSaves08" REL="nofollow" rel="nofollow">study by Vanguard</a>, only 10% of people max out their 401k. If you are one of the 10%, then yes, Roth means you can contribute more. For the other 90%, instead of contributing to Roth, they can also increase their 401k contributions. Then this math law applies. Kyle – I hear you. The contribution limit is a problem, but only if you hit the limit. If contributing to a Roth IRA means contributing more, you can also increase the contribution to the traditional 401k instead. According to this study by Vanguard, only 10% of people max out their 401k. If you are one of the 10%, then yes, Roth means you can contribute more. For the other 90%, instead of contributing to Roth, they can also increase their 401k contributions. Then this math law applies.

]]> By: kyle http://thefinancebuff.com/commutative-law-of-multiplication.html#comment-553 kyle Mon, 31 Mar 2008 18:21:00 +0000 http://blog.thefinancebuff.com/?p=126#comment-553 I disagree with your application of the commutative law to IRAs.<br/><br/>You're forgetting the effect of contribution limits. By using a Roth IRA you can pay the taxes from your other income, effectively increasing the amount you can contribute. If you put the money in a traditional IRA, on the other hand, you may end up paying taxes the taxes from your distributions if you don't other income to pay them. I disagree with your application of the commutative law to IRAs.

You’re forgetting the effect of contribution limits. By using a Roth IRA you can pay the taxes from your other income, effectively increasing the amount you can contribute. If you put the money in a traditional IRA, on the other hand, you may end up paying taxes the taxes from your distributions if you don’t other income to pay them.

]]> By: Anonymous http://thefinancebuff.com/commutative-law-of-multiplication.html#comment-175 Anonymous Wed, 27 Jun 2007 12:31:00 +0000 http://blog.thefinancebuff.com/?p=126#comment-175 Thank you for this post. The Simple Dollar is, for whatever reason, a very popular sight despite the fact that (1) his posts usually lack content and (2) when he does have something, he often gets it wrong. I've followed his logic with squinted eyes since the get-go.<br/><br/>That said, I have enjoyed your postings. Relevant and factual. And you don't feel some mandate to have six posts a day just to have six posts. Keeps it 'simple'.<br/><br/>-Mike Thank you for this post. The Simple Dollar is, for whatever reason, a very popular sight despite the fact that (1) his posts usually lack content and (2) when he does have something, he often gets it wrong. I’ve followed his logic with squinted eyes since the get-go.

That said, I have enjoyed your postings. Relevant and factual. And you don’t feel some mandate to have six posts a day just to have six posts. Keeps it ‘simple’.

-Mike

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