Contribute $A to TFSA
Grows at rate g for n years
Proceeds = A × (1 + g)^n

Contribute $A to RRSP
Grow at g for n years
Pay tax rate = tn upon withdrawal
RRSP proceeds = A × (1 + g)^n × (1 - tn)

Deduct $A from taxable income
Obtain refund of $A × t0
Contribute A × t0 to TFSA
Grows at rate g for n years
TFSA proceeds = A × t0 × (1 + g)^n

Total proceeds = RRSP + TFSA
= A × (1 + g)^n × (1 - tn) + A × t0 × (1 + g)^n
= A × (1 + g)^n × (1 - tn + t0)

A × (1 + g)^n × (1 - tn + t0)
= A × (1 + g)^n × (1 - t + t)
= A × (1 + g)^n

Those are tricky questions since question #2 and 3 require forecasting the future. You can make some approximations - are you currently in the 1st/2nd/3rd marginal brackets? Do you anticipate making less/same/more income in the future? Will that move you up/down the marginal brackets? Remember to also consider the impact of CCB benefits, GIS/OAS clawbacks, etc. Check out the calculator at rrspcontribution.ca and review the marginal tax rates at taxtips.ca.

We often see this question asked:

I'm currently making low income and expect a higher salary in the future. Should I contribute to an RRSP? Should I contribute and simply defer the tax deduction to a higher tax year?

It should be obvious that if you have sufficient TFSA room, you should always use the TFSA before RRSPs during periods of lower income. You'll likely withdraw at the same or higher marginal bracket, not lower, so TFSAs can let you arbitrage the difference in current vs. future tax rates. On the other hand, what happens if you don't have enough TFSA room?

To analyze this situation, some further assumptions:

• You have enough RRSP room to shelter $A

• You have enough TFSA room to shelter some portion of $A, but not all of it.

Let's suppose you contribute to a RRSP today and then wait "m" years before deducting at a higher marginal bracket.

Contribute $A to RRSP
Grow at g for n years
Pay tax rate = tn at withdrawal
RRSP proceeds = A × (1 + g)^n × (1 - tn)

Wait m years to reach tax rate = tm
Deduct $A from taxable income
Obtain refund of A × tm
Contribute A × tm to TFSA
Grows at g for n years
TFSA proceeds = A × tm × (1 + g)^(n-m)
= A × tm × (1 + g)^n ÷ (1 + g)^m

Total proceeds = RRSP + TFSA
= A × (1 + g)^n × (1 - tn) + A × tm × (1 + g)^n ÷ (1 + g)^m
= A × (1 + g)^n × (1 - tn + tm ÷ (1 + g)^m)

Notice that if m converges to zero (i.e., you deduct immediately), then tm = t0 and this expression is identical to one from above.

A × (1 + g)^n × (1 - tn + tm ÷ (1 + g)^m)
= A × (1 + g)^n × (1 - tn + t0 ÷ (1 + g)^0)
= A × (1 + g)^n × (1 - tn + t0 ÷ 1)
= A × (1 + g)^n × (1 - tn + t0)

This illustrates an important point:

• You can obtain a benefit from deferring the deduction: the differential between tm and t0

• However, this benefit must be discounted by the growing penalty of (1 + g)^m.

Many readers may already be familiar with this resource, which argues deferring the deduction is usually sub-optimal: https://www.retailinvestor.org/rrsp.html#delay

This is because you actually have three options when using a RRSP (where the TFSA is nearly maximized):

1. Contribute to the RRSP and deduct immediately

2. Contribute to the RRSP and deduct in the future

3. Invest in a non-registered account and defer contributing to the RRSP

This last option is complicated by the ongoing drag when investing outside of a registered tax shelter. Instead of realizing growth = g, you'll earn some different amount g* subject to the actual mix of eligible/non-eligible dividends, interest income, and capital gains/losses when you eventually move the funds into a registered account.

Invest $A in a non-registered account
Grow at g* for m years

Contribute the new amount to RRSP
Grow at g for n-m years
Pay tax rate = tn at withdrawal
RRSP proceeds = A × (1 + g*)^m × (1 + g)^(n-m) × (1 - tn)

Deduct from taxable income at tm
Contribute refund to TFSA
Grow at g for n-m years
TFSA proceeds = A × (1 + g*)^m × tm × (1 + g)^(n-m)

Total proceeds = RRSP + TFSA
= A × (1 + g)^n × (1 - tn + tm) × [(1 + g*)/(1 + g)]^m

Notice that if g* converges to g, then the expression becomes:

A × (1 + g)^n × (1 - tn + tm) × [(1 + g*)/(1 + g)]^m
= A × (1 + g)^n × (1 - tn + tm) × [(1 + g)/(1 + g)]^m
= A × (1 + g)^n × (1 - tn + tm) × [1]^m
= A × (1 + g)^n × (1 - tn + tm)

Which is superior to the deferred deduction expression! This means if you have low tax drag (e.g., mostly capital gains versus interest income), then deferring the contribution will yield a better outcome than deferring the deduction. On the other hand, high tax drag where g* is significantly less than g will yield a worse outcome (e.g., receiving interest income at a high marginal tax rate).

There is no general solution for g* versus g that gives the optimal decision. But, using this expressions will make it much easier for you to test a few numerical solutions, especially since the expressions can be further simplified.

Since "A × (1 + g)^n" appears in four expressions, we can replace it with the constant "B". This gives us:

TFSA only
= B

Contribute to RRSP with immediate deduction
= B × (1 - tn + t0)

Contribute to RRSP and defer the deduction
= B × (1 - tn + tm ÷ (1 + g)^m )

Defer the RRSP contribution and use a non-registered account
= B × (1 - tn + tm) × [(1 + g*)/(1 + g)]^m

There are just five variables of interest:

1. Withdrawal tax rate = tn

2. Intermediate tax rate = tm

3. Tax dragged growth = g*

4. Expected growth = g

5. Intermediate years = m

As an exercise for the reader, rewrite this as a ELI5.