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In a recent column, I wrote about an individual who had a large sum of cash and was planning to contribute part of it to a registered retirement savings plan.

Well, it wasn't long before the anti-RRSP crowd weighed in.

RRSPs are a terrible idea because "you lose the lucrative dividend tax credit and the 50-per-cent capital gains reduction," one reader wrote. Another said that contributing to an RRSP would "turn a tax-free windfall into taxable income when taken out of the RRSP."

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Nonsense.

I've been hearing these sorts of specious arguments for years, and no matter how many times I explain why they're wrong, they endure like the personal finance version of some scary urban legend. Why? Because RRSP bashers would rather complain about the tax they have to pay than take the time to understand how RRSPs really work.

So today – probably not for the last time – I'll explain how to do the RRSP math correctly. I'll also demonstrate why RRSPs are a great tax-saving tool for most investors.

Let's look at a simple example.

Assume an individual has saved $10,000 and she's wondering whether she should invest it inside her RRSP or in a non-registered account. We'll further assume her marginal tax rate is 40 per cent and that – regardless of what account she chooses to invest in – she buys a stock that triples in value over a 20-year period.

Would she be better off investing inside or outside her RRSP?

Now, before we tackle that question, we need to deal with the tax refund. Assuming her employer deducts income tax from her paycheque, if she contributes the $10,000 to her RRSP, she will receive a $4,000 tax refund. So, that $10,000 RRSP contribution wouldn't actually cost her $10,000; it would cost her just $6,000 ($10,000 minus the $4,000 refund).

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Stated another way, at a 40-per-cent marginal tax rate, $10,000 inside an RRSP (which contains pretax dollars) is equivalent to $6,000 in a non-registered account (which contains after-tax dollars).

Now, let's return to the example, using these numbers as our starting points. This is the only way to do a fair comparison.

First, investing inside the RRSP: The $10,000 would triple to $30,000 after 20 years. If she then sells the stock and withdraws the money, she'll pay $12,000 of income tax (40 per cent of $30,000) and be left with a net $18,000.

Now, investing outside the RRSP: The $6,000 would grow to $18,000 after 20 years. If she then sells the stock, she'll pay capital gains tax of 20 per cent (half of 40 per cent) on the $12,000 difference between her sale and purchase prices. After deducting $2,400 in tax, she'll be left with just $15,600.

Verdict: The RRSP produces a superior return. Notice that the difference between the RRSP and non-registered totals ($18,000 versus $15,600) is equal to the capital gains tax ($2,400) that applies in the non-registered scenario. Far from "losing the 50-per-cent capital gains reduction," the RRSP avoids capital gains tax entirely.

You can use any return assumptions you want, generated by any combination of capital gains, dividends and interest, and the RRSP will always come out ahead if you assume a constant marginal tax rate and if you start with amounts that are equivalent on an after-tax basis. That's because capital gains, dividends and interest are not taxed in an RRSP, but they are taxed in a non-registered account.

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With an RRSP, the only tax is on withdrawals. People love to complain about the tax on withdrawals because it looks so large, but it's really just the original tax they deferred plus the growth of that tax over time. As the example above showed, even after paying tax on withdrawals, the RRSP investor still wins. If an investor's marginal tax rate is lower in retirement, the benefit of RRSPs is even stronger.

What if someone's marginal tax rate is higher in retirement? Wouldn't that make RRSPs a bad choice? Not necessarily. Jamie Golombek, managing director of tax and estate planning with CIBC Wealth Advisory Services, examined various scenarios in this paper. His analysis showed that, even assuming a fairly drastic 10-percentage-point increase in the marginal effective tax rate (METR), RRSPs would still enjoy an advantage over non-registered accounts given a long enough investing horizon. That's because the benefits of tax-free compounding would eventually outweigh the impact of a higher METR on withdrawals.

The math behind RRSPs can be tricky. But if you take the time to read Mr. Golombek's detailed paper – and some of my earlier columns – you'll see that most anti-RRSP arguments are nothing more than investing urban myths.

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