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 Canaccord Genuity Corp.


Markus Muhs - Jan 06, 2022
Everything you want or need to know about TFSAs, in one place.
Updated for 2022
I’ve written a few times about Tax Free Savings Accounts here and have decided to finally put everything together into a TFSA wiki page, akin to my RESP wiki, which I’ll regularly update in the future. My aim is that if you have ANY questions about TFSAs, you’ll find the answer here and, and if you don’t, please send me a message: I’ll be happy to answer it for you directly, and you’ll be helping me out as I’ll add that answer to the wiki as well.
Just a warning that this post is a long one, but to help you find the answers to your TFSA questions, I’ll add a little menu below:




A Little History

The misnomered TFSA (it’s not a savings account!) came about from the 2008 federal budget, which was actually a pretty significant budget if memory serves. I believe it was the same budget that had some goodies for RESPs (additional CESG, more flexibility, higher limits) and where pension income splitting was introduced. Or it could have been the year after; in any case, my first few years as a financial planner coincided with a number of significant changes in the realm of personal financial planning.
Those who know me know I follow politics fairly closely, and I find in personal finance especially it can be advantageous to be in tune with political trends and the objectives of the mainstream political parties. During the 2006 federal election, the Conservatives made a pretty ambitious election promise (maybe they didn’t think they’d win) of scrapping capital gains tax. Delivering on a promise like that was not only impossible in the fiscal regard (losing a lot of tax revenue) but would have also been incredibly unpalatable if people with millions invested in stocks outside of their RRSPs all of a sudden get a massive tax break and the rest of us get nothing.
Instead, the TFSA was designed based on similar tax-advantaged account types in other countries. It's an account where everyone can save and invest money—up to certain limits—on a completely tax-sheltered basis. Like the American Roth IRA or British ISA, annual contribution limits for the TFSA started in the same neighborhood of $5000. TFSAs would be far more flexible than Roth IRAs though, as they allow withdrawals at any time, for any purpose, without penalty or taxation, whereas Roths continue to be seen as mostly retirement vehicles, with age requirements or special circumstances for penalty-free withdrawals.
Early on, the naming of the TFSA caused the greatest level of confusion for investors and frustration for advisors. Tax Free Investment Account, Tax Free Savings Plan, or simply Tax Free Account would have been how I’d have named it. The first questions I got from a lot of clients was “what interest rate does it pay?” and because the banks had their marketing ready to go on day one for TFSA savings accounts, a lot of Canadians missed out on getting the most of their new TFSAs, thinking that was their only use. I recall some studies done around 2010 or 2011 showing that most Canadians at that time still didn’t understand TFSAs and were unaware money in a TFSA could be invested just like in an RRSP.


The Basics

The most basic explanation of a TFSA is that it works just like having money in an investment or savings account outside of your RRSP, only the tax slips are switched off. Plain and simple, it’s a true tax shelter. 
You can open a TFSA if you're over 18 and are a permanent resident of Canada. Contribution limits count and accumulate for each partial or full calendar year in which you are/were a resident of Canada over 18. I’ll write a little more later on what happens if you leave Canada, or things to take into consideration for dual citizens, in particular, people classified as “U.S. persons”.
You don’t get anything tax-wise for putting money into a TFSA. No contribution receipt, no tax deduction as with an RRSP. Like in an RRSP, you don't get taxed on money while it is invested inside of the TFSA, and the major benefit is that you also don’t get taxed when you take money out of it. Whereas cumulative capital gains within an RRSP eventually get taxed as income when you withdraw from an RRSP/RRIF, in a TFSA such gains are taxed never.
As mentioned, there are limits to what you can put into your TFSA. This is to put most of us on an equal playing field, and not benefit high net worth people unfairly, who I’m sure would love to shelter ALL their money from taxation. You accumulate more contribution room in each year that you live in Canada as an adult, and this contribution room accumulates whether you use it or not. So, if you’ve been living in Canada since 2009, and were 18 or older in 2009, and have never contributed to a TFSA, your lifetime accumulated contribution room to date (2022) is $81,500.
The amount we can contribute annually started at $5000 in 2009, with the expectation that it would rise at the rate of inflation, in $500 increments. In 2015, which was an election year, the Conservative government raised this to $10,000. The ensuing Liberal government dropped it back down to the originally planned $5500 in 2016, giving the Conservatives the political fodder of "they took away your TFSA contribution limit". Really it just put us back on the original contribution pathway and nothing was "taken away" while the one time $10K limit in 2015 was a nice bonus. The full history of annual TFSA contribution limits is as follows:
2009: $5000
2010: $5000
2011: $5000
2012: $5000
2013: $5500
2014: $5500
2015: $10,000
2016: $5500
2017: $5500
2018: $5500
2019: $6000
2020: $6000
2021: $6000
2022: $6000
Total: $81,500
Contribution limits are expected to continue to go up every few years at $500 increments, based on inflation. Upon the announcement of the 2022 contribution limit there was some grumbling that, due to inflation, it should have been bumped up to $6500. I think the metrics they use are on a bit of a lag though, so it'll likely be that in 2023 the limit goes up to $6500. There’s always the chance that a future government changes this for the good or for the better. Again, being aware of different political party objectives can be useful in long-term financial planning:
  • The CPC prefers to raise the annual limit faster, allowing older Canadians (with fewer years left to accumulate contribution room) to shelter more of their investments.
  • The NDP thinks that the TFSA is a bad idea, unequally benefiting the wealthy, because saving $500 per month is in their opinion out of reach for most Canadians.
  • The LPC is somewhere in between, not wanting to benefit the wealthy too much with too-high contribution limits, but not wanting to upset many middle-class Canadians who take advantage of their TFSA contribution space annually.
Upon death of a TFSA holder, assets can flow tax-free to a beneficiary (if designated) or to the Estate. There’s a significant benefit to spouses designating each other as “successor holders” of their TFSAs, as then assets flow tax sheltered to the survivor as opposed to being removed from the TFSA and having to then be re-contributed, as is the case if anyone else is designated as beneficiary. What this means is if two spouses each have $100,000 sheltered in their TFSAs and one dies, the survivor ends up with a TFSA of $200,000, fully sheltered and without any impact on contribution limits.


Contributions & Withdrawals

You can open as many TFSAs as you want, at multiple institutions. How are your contributions tracked? They’re reported directly by each financial institution to the CRA. You can find out what your contribution limit is by going to the CRA’s My Account for Individuals, but keep in mind that there’s always a lag (usually half a year or more) between when you transact on your TFSA(s) and when it reflects on the government website.
Contributions and withdrawals are where I find people have the most questions and where they commit the most errors. Unlike an RRSP, the CRA doesn’t give you a $2000 cushion for over-contributing; you just get an angry letter from them. It used to be they’d go straight to penalizing you, but for some time now they have simply been sending a warning letter on the first offense (instructing you to remove the over-contribution as soon as possible), but I believe you only get warned once.
Like an RRSP, the penalty on over-contributions is 1% of the over-contributed balance for each full or partial month it remains in the plan.
When money is withdrawn from a TFSA, that amount can be re-contributed in the following calendar year. It simply gets added to your contribution limit in the new year, along with your new annual contribution space. There was some confusion in the early years of the TFSA as to how investment growth factors into this. For example, if $5000 contributed in 2009 doubled to $10,000 and was then withdrawn before year end, is the 2010 contribution limit $10,000 (original $5000 plus new 2010 limit) or $15,000 (2010 limit plus the $10,000 withdrawn)? Quite simply, it’s the latter: whatever dollar amount was withdrawn gets added to contribution room the following year. This can work both ways: if you lose money in your TFSA, that contribution space is lost forever, you don't get a mulligan.


What Can a TFSA Be Used For?

Absolutely anything! That’s what makes the TFSA so great, relative to other registered plans and even compared to similar plans around the world. There are no penalties to withdraw, no taxation, and you don’t need any special reasons to withdraw money from the plan.
For a young person just starting out, the TFSA is a great place to house your emergency fund. As I’ve mentioned in other blog posts, I believe it’s absolutely crucial that anyone and everyone establishes a solid emergency savings fund before embarking on any and all other savings goals. Do not put a penny into your RRSP and don’t even think about investing in stocks or equity funds until your emergency savings are well funded! You’ll never know when you might need them (ie: when a completely unexpected global pandemic hits and you lose your job) and money in retirement accounts or invested in equities are not (should not be) accessible on short notice.
Savings accounts pay very little interest though, so for a more established investor with a well-funded RRSP, emergency savings, and additional money to invest long-term, it is best they pivot the use of their TFSA toward long term investing and leave their emergency savings effectively unsheltered. A mistake made by many Canadians, again because of the mis-naming of the TFSA as a “savings account”, is that they either outright believe that the TFSA is only for short-term savings, or they just don’t pivot it to longer-term use, once they have the financial wherewithal to do so.
To clarify, if you have money outside of your RRSP that is meant to be saved for the long-term (more than 10 years), this is what the TFSA is best used for, while emergency savings at pathetically low interest rates are best kept outside of a TFSA (you don’t save a lot of tax when earning less than 1% interest). If emergency savings is all the cash you have outside your TFSA, you should keep using the TFSA for this money until you have enough of an excess saved up.
I could give a long list of different savings goals you can direct a TFSA toward—and sure, you can use it to save up for a car, just don’t invest it too aggressively if that goal is less than 10 years away. It benefits you the most, the longer term your savings goal is.
Think again of how a TFSA works and how the Tax-Free-ness actually benefits you: You don’t get a tax deduction when you contribute to it, like with an RRSP. You do avoid paying tax on investments as long as they are sheltered inside of it. Ipso facto, you benefit the most the higher your rate of return, and the longer money stays sheltered in it. Your deadline for taking money out of the TFSA is not age 71—as with an RRSP—your deadline is DEATH!
Ultimately, our long term goals should be not just to maximize our TFSA contributions, but to grow that bucket of wealth as much as possible. All that growth stays sheltered in the TFSA and continues to compound tax free as long as it’s in there.
Let’s just look at what the difference of a few percentage points of growth can mean over the long-term. $5000 contributed annually into a TFSA at a low 1% savings interest rate versus a modest 5% average growth rate on an investment portfolio over 30 years.
  • Savings: TFSA builds up to a little over $175,000 ($25,000 of tax free interest income)
  • Invested: TFSA builds up to nearly $350,000 ($200,000 of tax free investment income)
In a well-constructed financial plan, different buckets (ie: RRSP assets, TFSA assets, etc) can have different time horizons applied to them and it behooves the investor to assign as long a time horizon as possible (allowing them to take greater risk) to their TFSA assets. If you make it all the way to the bottom of this page, my Tax Free Legacy Plan goes into this in more detail.
Should you buy highly speculative penny stocks in your TFSA? That can literally be a hit or miss proposition. Yes, a ten-bagger (an investment that multiples in value by ten) can be highly beneficial held within a TFSA: imagine investing $10K into a stock in a TFSA and now having a $100,000 TFSA! Losing all your money on an investment in a TFSA can be highly detrimental though, as you’ll never get that contribution room back and you can’t use that capital loss against any gains.



Obviously a common pitfall with TFSAs is one I’ve already covered above—that is over-contributing to one—but how does this usually happen?
A common way people over-contribute is by having multiple TFSAs at multiple institutions and just losing track of their limit. If you’re going to have more than one, the onus is entirely on you to keep track of this all; no one else will, least of all each of the institutions who aren’t communicating with each other. Moving a TFSA around from institution to institution also causes confusion.
Another common way over-contributions happen—this happened a lot in the first few years of TFSAs when people treated them like savings accounts—is simply through continuous money-in, money-out transactions throughout the year. Many banks also didn’t have systems and training in place to help prevent their customers or their tellers from making these mistakes.
As mentioned, in the section above on contributions/withdrawals, you can only contribute back your withdrawals from a TFSA in the following calendar year. So, what happens when someone uses the TFSA like a savings account, regularly contributing money, occasionally tapping into those savings, and then putting the money back a few months later? Overcontributions! For example, assuming a $6000 available limit at the beginning of the year:
  • $2000 contributed in January
  • $2000 spent on vacation in February
  • $2000 put back into the plan in March
  • Another $2000 contributed in July
  • $2000 taken out for Christmas gift shopping in November
  • $2000 year-end bonus contributed in December
In the above example, the person contributed net $4000 over the course of the year, but in the eyes of the CRA they contributed $8000; a $2000 over-contribution for which they'll be penalized $20 (only for the month of December). In actual practice, this was happening with smaller and more frequent transactions, until the banks started to add better disclaimers to their online banking, when people make contributions, and a bank I worked at also added a “flag” that pops up whenever tellers make transfers into TFSAs.
Taxable Tax Free Savings Accounts
TFSAs are also not guaranteed to be tax-free in all cases. The CRA can determine day-trading activity within a TFSA to be of a “professional” nature and, just as they can disqualify you from the 50% capital gains inclusion rate, they can disqualify such assets from tax sheltered status. So, in the above example of having a ten-bagger stock within your TFSA, having a few of those, or just too much luck at day trading, can lead to the CRA assessing your gains as income. It's a grey area, but it's their call really, not yours.
An investment can also become ineligible for a TFSA and suddenly draw a penalty tax as with an over-contribution. I had this happen to myself back in the early days, when a small TSX Venture listed stock that I held in my TFSA suddenly was taken over by a Swedish company. While it was expected that the company would be dual-listed on the TSXV and the Swedish equivalent exchange, in the end they decided to drop the TSXV listing. While stocks listed on major stock exchanges around the world are eligible to be held within TFSAs and RRSPs, those listed on junior exchanges (other than the TSXV) generally aren’t. So, through no fault of my own, my eligible TSXV listed stock became an ineligible TFSA investment and I got a letter from the CRA forcing me to remove it and pay tax on the gains (from the date when it became ineligible).
U.S. persons may also find their TFSAs aren’t completely tax free. A U.S. person is generally someone with U.S. citizenship or a Canadian who has become a resident of the U.S. and pays tax there. Unlike with RRSPs/RRIFs, there is no tax treaty between the U.S. and Canada on TFSAs, so the IRS doesn’t recognize them as tax shelters. In their eyes, these are essentially taxable non-registered investments. A Canadian who moves to the U.S. can’t contribute to a TFSA anymore anyway, and might as well just close down their TFSA, but for a U.S. citizen permanent resident of Canada or dual-citizen there may or may not be any benefits to investing in a TFSA, depending on how their taxes shake out. Such people would still file in the U.S. based on their worldwide income, but taxes in Canada are generally higher and the deduction on foreign taxes paid (in Canada) can more than offset taxes due on investment income within the TFSA, yielding nothing owing to the IRS. Everyone’s situation is different though and so this is where I’d really suggest speaking to a cross-border tax specialist.
On a related note, U.S. dividends earned in a TFSA are not exempt from the IRS 15% withholding tax, as they are in an RRSP. This applies to everyone, not just U.S. persons. 


RRSP or TFSA for Retirement?

The TFSA can be an incredibly powerful tool for retirement planning, and this is where I think it benefits the middle-class the most, as for Canadians below a certain income level it can benefit them more than an RRSP when used for retirement saving.
Keep in mind that when saving money via an RRSP your "tax savings" in the year you make an RRSP contribution are not your full permanent tax savings. What you actually save in taxes is the product of a more complex equation that takes into account the immediate tax savings, the taxes you'll eventually pay when you draw the money out of your RRIF when you're retired, and the effects of tax-deferred compounding of your investment income while in the RRSP/RRIF.
Let's assume, as an example, you're earning $150,000 per year gross in Alberta and have a combined federal + provincial marginal tax rate of 38% (on income from around $130K to $150K). Contributing $20,000 to your RRSP eliminates all the income on which you pay the 38% rate on, reducing your tax bill by $20,000 x 38%, or $7600. When you're retired, if you can keep your taxable income (inclusive of RRIF income) to under $50,000 (based on current tax brackets), all your retirement income ends up being taxed at 25% or less, so what comes out of your RRIF gets taxed at 25%. Assuming all else is equal: 38 cents for every dollar put into the RRSP, 25 cents per dollar taken out (or 30.5 cents if your income is somewhere between $50K and $100K, approximately). Add to the list of benefits the tax-deferred compounding of investments within the RRSP (that $20K will hopefully be $60K-$100K in 20 years) and the potential that you could have invested that $7600 of initial tax savings over 20 years and the RRSP contribution overall nets out quite a benefit to the saver. So, if such a saver—in this example—only had $20K to save for retirement and had to choose RRSP or TFSA, the RRSP should be a no-brainer. If they can save more, then they should consider both
Now, let's look at the example of someone earning $49,000 per year gross. I'm using that number because it's just barely within the first marginal tax rate in Alberta, of 25% on earnings between $19,370 and $49,020 (2021). They have $6000 to save for retirement and must choose between RRSP and TFSA. Putting that $6000 into an RRSP only nets an immediate savings of 25 cents for every dollar put in, which might seem like a nice extra tax refund, but keep in mind that when this person is retired they likely will be in the same tax bracket, possibly even higher; they don't keep that $1500 forever. If the saver's marginal tax rate during retirement is also 25%, and they invest the $1500 refund, then whether they use a TFSA or an RRSP is a complete wash in the end (more taxes saved over time in the TFSA make up for the extra $1500 invested, in the end).
When all else is equal, the downside of saving with an RRSP for retirement vs TFSA, is that the RRSP creates taxable income in retirement, while using a TFSA avoids taxes entirely. Presuming OAS is still around in 20 years and follows the same income-test for eligibility (instead of an asset-test), one can save a large amount of money over time in a TFSA ($6000 saved annually for 30 years, compounded at 6%, works out to over half a million) and, with only CPP income otherwise, live reasonably comfortably in retirement and pay very little tax. Beyond just keeping your retirement tax bill to a minimum, there are various benefits offered (or which may be offered in future) by federal and provincial governments that are income-tested, such as drug plans, or possibly even the Guaranteed Income Supplement if your CPP income is low enough and there is no other income.
Beyond this, if two spouses earned incomes of around $48K or less during their working years and saved only in their TFSAs, not in their RRSPs, there are significant benefits in terms of how a surviving spouse is taxed, and how the final Estate is taxed when using TFSAs. Consider that, while only saving 25 cents for every dollar put into their RRSPs during their working lives, one spouse dies in early retirement: the surviving spouse might then be drawing out of a combined RRIF at a marginal tax rate of higher than 25%, and if they also die fairly young (before much of the money is withdrawn) the lump sum remaining in the final RRIF could be taxed at even higher rates at death (RRIFs are taxed all at once at death, unless rolled over to a surviving spouse, and are subject to our progressive marginal tax rates).
The bottom line is that if you expect your marginal tax rate in retirement to be roughly the same as it is now, there are more benefits to saving using a TFSA and foregoing RRSPs entirely. If your income is fairly high now, and you expect your marginal tax rate to be lower in retirement, you can prioritize saving via an RRSP, but can probably afford to max out both anyway. A good resource for determining your tax rates (now and maybe what they'll be in the future) is Ernst & Young's Tax Calculator page.


The Tax Free Legacy Plan

If your immediate short-term and medium-term goals are all met, then the only logical purpose for the TFSA is to fund your longest term goals: late retirement income and your legacy.
A sensible retirement income plan over a 30 year+ retirement should involve, over time, drawing down assets in the most tax-efficient manner possible. Tax-efficiency needs to be taken account in the long-term perspective more so than short-term year to year.
A typical retired person without a defined benefit pension plan is generally funding their retirement income from three buckets: non-registered investments, RRSP/RRIF, and TFSA. I’ve found that many without a proper retirement income plan tend to have a short-term tax perspective and prioritize where they draw money from as follows:
  • Defer converting the RRSP to RRIF as long as possible (age 71) in order to defer taxes as long as possible, then only take minimum payments.
  • Use up non-registered assets in early retirement: these are easily accessible and draw annual taxation on investment income, so you might as well use them up.
  • Use TFSA assets also, or stop contributing to it after retirement, or direct it to shorter-term goals.
The above is all wrong—sorry if I briefly misled you—and on top of that, when I wrote my blog post on when to start CPP I also found that the stats show that Canadians tend to start their CPP way too early, but that’s another thing. There may be cases where all of the above is the right strategy for someone, but for most it is a symptom of short-term thinking.
Assume a couple are retiring at 65 and expect to live till 95, and they have $200,000 of non-registered investments, $600,000 of RRSP investments and have $75,000 in each of their TFSAs. I ran a couple of retirement scenarios on NaviPlan (to whom I attribute the below graphs) for this hypothetical couple; one where they follow no strategy (the bullet points above, "Current Plan" in the graphs below) and one where they follow a strategy that I outline below (Proposed Plan). For simplicity, I nixed out inflation in the plan and have all accounts growing at an even 3% per annum (5% minus inflation, roughly) and set their retirement expense goal at $3000 per month. We’re also not including CPP/OAS or any other incomes in the plan, to keep it simple. The plan automatically applies tax rates for Alberta residents to both scenarios, including their Estates, and automatically applies pension income splitting where/when appropriate.
A proper strategy, making full use of their TFSAs and minimizing taxes on their estate at the expense of a bit more annual taxation in their first 20 years of retirement is as follows:
  • Convert RRSPs to RRIFs immediately at retirement and draw out more than the RRIF minimums; enough to draw them down entirely by the time you’re in your 80s and are more likely to expire.
  • Draw from non-registered investments to make up the difference in expense needs.
  • Keep maxing TFSA contributions annually for the rest of your life or until the other buckets run out of money; only then draw from your TFSA.
The net effect, as mentioned, is a little bit more tax year by year as the couple draws more out of their RRIFs. Overall everything is growing at the same rates though, and the couple’s spending is the same in both scenarios. By effectively reducing the final tax bill due on whatever’s left in their RRIFs in their 80s, and by shifting all their remaining assets into TFSAs, they reduce the final tax bill on their Estate to zero (again this isn’t taking into account any other assets or income that I omitted to keep things simple) and their Estate ends up over $100,000 richer. Partially contributing to this as well is the fact that money doesn’t linger in the taxable joint account as long (it gets shifted over into their TFSA, as contribution limits allow) and in their final retirement decade the couple pays no taxes at all, as income is only drawn from TFSAs (RRIFs and non-registered have depleted by then).
Again, this is a very simplified scenario, but it exemplifies the power of a TFSA over the long-term, when utilized correctly. Add to this scenario the ability to take a bit more risk and achieve a higher rate of return on TFSA assets, as you have a longer time horizon on that particular bucket (even at retirement, the couple can consider TFSA assets to have a 20 year time horizon). 
I should reiterate that the main goal of your retirement planning should be partially to manage your taxes throughout retirement by being smart about where you draw money from (don’t defer your RRIF conversion to 71 if you’re fully retiring at 65!), but also to minimize taxes on your Estate (plan for what happens after retirement). The ideal Estate is one where all or most of your assets of the last to die spouse are tax free: in TFSAs and a principal residence. The graphs below show the difference that the above strategy can have on final Estate taxes, with red bars reflecting final Estate taxes (if both spouses die that particular year) and the green line representing the after-tax Estate. In dollar terms, it's the difference between an after-tax Estate of $530K vs $420K at age 95 (2050), or $685K vs $500K in 2041.
To reiterate, in the two scenarios above the starting assets, investment growth rates, and annual spending are identical. The only difference—leading to a considerably higher after-tax Estate—is the order in which assets are used in retirement, and making full use of the TFSA.
Where late retirement tax planning is concerned, the above strategy also benefits the surviving spouse of the typical retired couple. Once one spouse dies, the surviving spouse will often be shocked with their tax bill in their first full year as a widow/widower. Where previously pension income (including RRIF income) was split evenly and thus taxed at relatively low marginal rates, the survivor has their pension income taxed only in their own name and thus can be taxed at higher marginal rates, in some cases even causing OAS clawback. Drawing only the minimum from RRIFs leaves a considerable amount behind when one spouse dies (say, in their early 80s) and the surviving spouse has to continue drawing the same gross amount out of those combined RRIFs and pay considerably more tax on those withdrawals. Better to have the RRIFs more depleted in favor of more money built up in the TFSAs in case either or both spouses do live long.



If you made it this far, congratulations: you probably know everything there is to know about TFSAs now. Do you still have questions? Please, go ahead and ask them on the form on my contact page. I won't hesitate to reply directly with the answer (if I know it) and your question gives me a guide as to what people are asking about TFSAs, so that I can make this page even more comprehensive.
The Tax Free Legacy Plan is incorporated in most of my retirement plans (where possible/feasible) and if you'd like to see how it would work in your own particular circumstances, I offer financial planning on a fee for service basis as well as on a percentage of assets under management basis. You can set up a complimentary 30-minute zoom call via my contact page as well to find out more.

Markus Muhs, CFP, CIM



None of the aforementioned should be construed at specific tax or legal advice, as everyone's situation is different. Have a personalized financial plan done with a Certified Financial Planning professional, such as myself, and consult with tax and legal specialists as needed. Assumed growth rates are examples only; when used in comparisons above a lower or higher growth rate does not materially affect the strategies discussed when both rates are equal.

Pictures used are my own or sourced freely through Pixabay. Graphs sourced through a licensed Naviplan account.