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Posted by cballard@tyyni.net on April 13, 2007, 3:30 am
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> I've been thinking about the value of a traditional vs. Roth
> IRA for my sons, who are just starting out. In the process
> I came to the conclusion that one is not automatically
> necessarily better than the other, even for young people. In
> fact, given two simple assumptions, both types of IRAs give
> EXACTLY the same results upon retirement. Under these
> assumptions, the "tax-free accumulation" advantage of the
> Roth is balanced by the tax-deductible feature of the
> Traditional. So this is yet another decision where the
> "right" answer is "it depends" and the facts necessary to
> make the right decision do not exist, since they lie in the
> future.
>
> Assumptions:
>
> 1) A fixed amount of pre-tax money to fund the IRAs. Say
> $3000.
>
> 2) The same marginal tax rate now and when the person
> retires. Say 20% for this discussion.
>
> If a Traditional IRA is opened with $3000 at 5% APR,
> compounded monthly, it will grow to $13,403.23 after 30
> years. After 20% income tax, the IRA will be worth
> $10,722.59.
>
> If the same $3000 is used for a Roth, the taxpayer first has
> to use $600 of the $3000 to pay the taxes on the $3000 that
> is not being deducted from his or her income, so they get to
> invest $2400 in their Roth IRA. After the same 30 years at
> the same 5% this grows to the same $10,722.59.
>
> Of course, if $3000 is invested in a Roth it will be more
> valuable after 30 years than $3000 invested in a
> Traditional, but this is not a fair comparison since the
> funds used to pay the current income tax on the $3000 are
> not being accounted for.
Your math is correct, but your analysis only applies if all
of the money that you have to invest is going into an IRA.
If you are keeping money outside of an IRA (and if those
funds are available to pay the taxes on the amount invested
in the Roth IRA), then the Roth IRA comes out ahead. Let's
modify your example a little and say that you have $5,000
that you are going to invest and that the maximum IRA
contribution is $3,000. I'll use the same 20% tax bracket
and 5% growth rate (compunded monthly) that you did.
With a regular IRA, you put $3,000 into the IRA (free of
tax) and the other $2,000 goes into an outside investment.
The $2,000 is subject to $400 of tax, leaving $1,600 to be
invested. The $3,000 in the IRA grows to $13,403.23, as you
indicated, but you have to pay tax on the withdrawal of
$2,680.65, leaving $10,722.59. The $1,600 in the taxable
account grows by 5% compounded monthly each year, and each
year that growth is taxed at 20%. Over 30 years this
account will grow to $5,330.40. The total amount, after
taxes, at the end of the 30 years is therefore $16,052.99.
Now, if we use a Roth IRA instead of a traditional IRA, you
put $3,000 into the IRA, and the other $2,000 goes into an
outside investment. The entire $5,000 is subject to $1,000
of tax, leaving $1,000 to be invested. The $3,000 in the
Roth IRA grows to $13,403.23, which can all be withdrawn
free of tax. The $1,000 in the taxable account grows by 5%
compounded monthly each year, and each year that growth is
taxed at 20%. Over 30 years this account will grow to
$3,331.50. The total amount, after taxes, at the end of the
30 years is therefore $16,734.73.
Investing in the Roth in this case yielded an extra $681.74.
That is the same as investing the traditional IRA and
getting a 5.149% yield (compounded monthly) rather than a 5%
yield.
As long as you have excess outside money to pay the taxes
with, the Roth IRA will beat out the traditional IRA,
assuming that the performance of the investments is
identical and that the tax rates stay the same. If there
are no outside investments, then the Roth IRA and the
traditional IRA will have the same performance. The
traditional IRA will never beat the Roth IRA. (Of course
this is making a big assumption: that tax rates are not
lower when the IRA withdrawals are made).
--Chris
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