Hopefully I have given you enough tease to get you curious about the tax advantages of a retirement savings account. I recommend you peruse these introductory posts to gain a basic understanding of retirement saving before reading this number-heavy post.
Why you should start saving early for retirement
Why retirement saving is not just about saving
Chances are you have heard about the tax advantages of a 401(k) or IRA somewhere before. Let me sum up and illustrate in an easy-to-understand way, and as always, I’m available to answer questions.
Let’s clarify this first: retirement savings accounts have tax advantages over what?
Let’s back off a little bit. Retirement saving is one of the ways of building wealth throughout your lifetime. Instead of saving for retirement, you can also start a business, buy a house, or win a lottery. Whatever way you choose to accumulate wealth, you pay the government taxes.
Saving for retirement is really investing in securities (stocks, bonds, etc.). To invest in securities, usually you need to open and contribute to an individual brokerage account. But retirement savings accounts provide an alternative that charges you less in taxes.
Retirement savings accounts have tax advantages over regular brokerage accounts.
Suppose you want to invest through a regular brokerage account. Well, the money comes right out of your income which is reduced by income taxes. Then, when your investment grows, the investment return gets taxed for capital gains. So going from salary to investment return, your income gets hit by two levels of taxes: income tax and capital gains tax.
For example, assume your annual salary is 50k, your income tax rate is a flat 20%, your rate of return on investment is 10%, and capital gains tax rate is a flat 25%. You want to invest 10% of your salary and withdraw everything after a year.
10% of your salary is 5k, but this amount gets reduced by 1k income tax, so you only have 4k to invest. You invest 4k and make $400 in return. The capital gains tax is $100. So when you withdraw next year, you will end up with 4.3k.
The retirement savings accounts get rid of capital gains tax. The difference between the Traditional 401(k)/IRA model and the Roth 401(k)/IRA model lies in when you pay the income tax.
In the Traditional model, you pay income tax when you withdraw only; the contribution is income-tax free. Let’s see how this works using the same numbers as above. You make 50k, and you contribute 10% of this which is 5k; this 5k does not get reduced by income tax, so you will have the whole 5k to contribute to the Traditional account. Your investment return is $500, so you will have 5.5k in the account next year. When you withdraw next year, the 5.5k amount is subject to income tax; at 20% that is 1.1k. So you end up with 4.4k.
In the Roth model, you pay income tax up front, but the withdrawal is income-tax free. Let’s use the same numbers as before. You want to invest 10% of your salary which is 5k, but you pay 20% of income tax on this and invest the rest which is 4k. Investment return is $400, so you’ll have 4.4k in your account. Withdrawal is tax-free, so you end up with 4.4k, the same as in the Traditional model.
If it is not clear why you end up at the same place in both the Traditional model and the Roth model, let’s set up a mathematical equation.
S: the pre-tax income you want to save for retirement
t: the income tax rate
g: the capital gains tax rate
r: the investment return rate
In the Traditional model, you can invest S, have S*(1+r) in the account, and end up with S*(1+r)(1-t) at withdrawal.
In the Roth model, you can invest S*(1-t), have S*(1-t)(1+r) in the account, and end up with S*(1-t)(1+r) at withdrawal.
So the Roth and the Traditional plans take you to the same place.
If you invest using a regular brokerage account, you have S*(1-t) to invest and have S*(1-t)(1+r) in the account, but when you withdraw you have to pay capital gains tax which is S*(1-t)*r*g, so you end up with S*(1-t)(1+r) – S*(1-t)rg, which is less than in the Roth or Traditional model. The shortfall is the capital gains tax.
The bottom line is, the tax advantage of a retirement savings account is really the elimination of capital gains tax.
If anything is not clear, let me know in the comments.
-Richard (Hiep Tran)
Hiep's Finance 
This has several incorrect premises. First, this article assumes the money is taken out one year later without any regards to compound interest. Second, this makes a false comparison between accounts of different amount of contributions.
The real question is this: with same amount of contribution growing to same amount of final result, how much tax do you pay when you take out the money? Let’s say base income is $50k, income tax bracket for $50k is 20%, contribution is $5k upfront, annual growth rate 7.2%, and taking out 10 years later (for convenience of calculation). $5k grows to $10k in 10 years with 7.2% growth.
With Roth model, in order to contribute $5k you must have pretax money of $6250, and consequently the total tax you pay is $1250. With Traditional model, you pay 20% of the result as tax which is $2k if tax bracket is the same, and even higher if (base income $50k + income from growth $10k) results in a higher tax bracket.
sakleewp, the compound interest for the one year is the investment return, which I assumed to be 10% to make matters simple.
In your example, assuming the tax bracket stays the same, investing in the traditional IRA results in 10k pre-tax, which is equivalent to 8k post-tax, as you pointed out. Investing in the Roth IRA, you’d have to pay 20% tax up front, so the 5k pre-tax becomes 4k post-tax. This 4k post-tax grows to become 8k, post-tax. So, if we assume the same tax bracket, both investment schemes take you to the exact same place. It doesn’t matter whether you pay income tax at deposit time or at withdrawal time, you’ll end up with the same amount of money. When you invest in a Roth, don’t forget that the income tax you paid upfront reduces the investment returns you would have gained had you selected to pay the tax later.