RRSPs and TFSAs are Mathematically Equivalent!

The introduction of the Tax Free Savings Account (TFSA) in 2009 has also introduced an additional complication for Canadians when it comes to deciding which accounts to invest in – RRSP or TFSA?

RRSPs and TFSAs are mathematically equivalent as I will demonstrate shortly, though it may not intuitively seem so.  The main factor that determines the better option between the two simply boils down to your current and expected future tax rates, all else being are equal.

RRSP and TFSA Characteristics

Lets first review the basic characteristics of these two types of accounts.

—RRSP
  • —Contributions to RRSP accounts reduce your taxable income
  • —Investments within RRSP accounts grow tax free
  • —Withdrawals get taxed at your marginal tax rate in the year of the withdrawal;  Contribution room is not restored after withdrawal
  • Contribution room depends on your income and how much room you have used up in the past
——TFSA
  • —Contributions do not reduce your taxable income
  • —Investments within a TFSA grow tax free
  • —Withdrawals from TFSAs are tax free; Contribution room in the amount of the withdrawal is restored in the following calendar year
  • —As of 2013, annual contribution room is $5500.  Cumulative room since the introduction of the TFSA is $25500

The Math

Let’s go through a simplified example to show how the two accounts are effectively equivalent.

We will use the following assumptions in the example:

  • Your total pre-tax income in the current year = $5000
  • Your marginal tax rate in the current year and in one year from now = 30%
  • You will earn a 10% return per year in whichever account you choose to invest
  • You will invest for a period of only 1 year
  • You will not get taxed on the $5000 income till you decide which option you will choose, RRSP or TFSA
Choice 1:  Put the full income into an RRSP
With this choice, lets suppose you decide to contribute your full $5000 income into an RRSP account.  Since putting this into an RRSP will reduce your taxable income by $5000, your net income for the year will be $0 and you will not have to pay any tax on the $5000 income.

Now, using our assumptions outlined earlier
  • Deposit —$5000 in RRSP, earning 10% in 1 year = $5000 * 1.10 = $5500 
  • —Withdraw from RRSP after 1 year – pay 30% tax = 30% * $5500 = $1650
  • —Ending Balance In Your Pocket = $5500 – $1650 = $3850
Choice 2:  Contribute to the TFSA
With this choice, lets suppose you decide to contribute your TFSA instead.  This means the government will first want to tax your $5000.

Again, using the earlier assumptions
  • —Pay 30% income tax = $5000 * 30% = $1500
  • Invest remaining amount in the TFSA = $5000 – $1500 = $3500
  • $3500 in TFSA, earning 10% in 1 yr = $3500* 1.10 = $3850 
  • —Withdraw $3850 from TFSA and pay no tax
  • —Ending Balance In Your Pocket = $3850
So as you can see, as long as your tax rates between the time you make contributions and the time you withdraw your funds don’t change, it makes no difference whatsoever where you invest your your funds.  You end up with the same amount of money!!

The premise behind investing in an RRSP is that during retirement, you will have a lower income and thus pay less tax when you withdraw money compared to when you put the money in (and thus getting a bigger tax break).

Since we can’t predict what our future income or future tax rates will be, we can use the following guideline to decide which account to invest in.  If you are in a relatively high tax bracket today, contributing to an RRSP will probably be more beneficial to you.  If you are in a relatively lower tax bracket, the TFSA will probably be more beneficial.
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