# Basic RRSP contribution math



## Dave (Apr 5, 2009)

Lets take a hypothetical 1000K RRSP contribution example. Correct me if I am wrong:

- When I contribute to the RRSP, I reduce my income by 1000K

- If I cash out the RRSP the year after, I will add the 1000K + gains to my income (equivalent to being taxed as interest)

It is a scary thing to contribute to the RRSP when you are young. Heck, I am not even sure if I will be alive when I will hit 70 (or able to enjoy the money  I have an over 70K contribution room, the cash, and a mental block the size of the Chinese wall. Sight... Just checking that I will not be hugely penalized if I chicken out of the RRSP thingy in a few years.

Dave


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## slacker (Mar 8, 2010)

The mental block is that people tend to see the tax refund as "free money", and then when they cash out the RRSP conveniently forgotten that they haven't paid income taxes on that money yet. It's a sweet deal that government had generously provided for people.

Regarding whether to use RRSP or not. The only relevant question (math wise), is whether your tax rate will be higher when you withdraw than when you contribute.

If it's higher, then don't use RRSP. If it's lower, then use RRSP.

Of course this has to do with a future unknown tax rate, so you're right to be nervous.


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## ChrisR (Jul 13, 2009)

It may seem a little scary to lock away your money when you're young, but you'll find that age creeps up on you pretty fast. It'll be a lot scarier if you skip saving and end up living on OAS and GIS in your golden years!


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## the-royal-mail (Dec 11, 2009)

If you are worried about this I would recommend a TFSA instead.

RRSPs are not meant for people who think they will "chicken out in a few years". They are intended as retirement savings and should not to be touched in most cases.


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## slacker (Mar 8, 2010)

One more clarification. RRSP is not locked in, and there is no penalty for withdrawal.

RRSP offers you the chance to skip out on taxes that you owe to the government for a long long time, decades if you wish. The only catch is that, you'll have to pay that tax sometime later, at a time of your choosing.

So just stop looking at the RRSP tax refund as "money gained", rather just as an accounting procedure that enables you to not get taxed right now, but to be taxed later.

TFSA is a perfectly good alternative for almost everyone, if the concept of tax deferral concerns you.


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## jamesbe (May 8, 2010)

People do this? IE: Put in $1000 this year to get a "tax break" then take it out to get the money back???


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## Donny (Dec 14, 2011)

slacker said:


> Regarding whether to use RRSP or not. The only relevant question (math wise), is whether your tax rate will be higher when you withdraw than when you contribute.
> 
> If it's higher, then don't use RRSP. If it's lower, then use RRSP.


That's true if you're comparing an RRSP to a TFSA. In that case, if you know your tax rate will be lower when you withdraw then you should use the TFSA instead of RRSP.

But, if your TFSA is full and you're comparing an RRSP to a taxable account, it can still make sense to use an RRSP instead of a taxable account even if you know your tax rate will be higher on withdrawal because of the tax-free compounding inside of the RRSP.


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## the-royal-mail (Dec 11, 2009)

Donny, how is "tax-free compounding" inherently any kind of an advantage? The compounding is NOT tax-free because you have to pay tax on every penny you eventually withdraw from the RRSP, whether it got there through compounding or not.


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## steve41 (Apr 18, 2009)

In reverse order of effectiveness.... non-reg, RRSP, TFSA. (where the last two are in an almost dead heat. Also.... it is virtually impossible to project a plan where tax rates in retirement are higher than pre-retirement. It simply doesn't happen. I will qualify that by stating that this is for 'saving for retirement' folks.... those who deplete or at least reduce their savings in retirement.


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## Donny (Dec 14, 2011)

the-royal-mail said:


> Donny, how is "tax-free compounding" inherently any kind of an advantage? The compounding is NOT tax-free because you have to pay tax on every penny you eventually withdraw from the RRSP, whether it got there through compounding or not.


Consider bonds in a taxable account. They pay interest every year, and you have to pay tax on that immediately. In an RRSP, you get the interest payment and do not have to pay tax on it (until you withdraw). Here's an example with numbers:

(Note: this is not a fair comparison between RRSP and taxable since in the real world your taxable starting balance would be (RRSP * (1-currentTaxRate)), but it just makes the point stronger).

Assuming you have $1000 in an RRSP vs $1000 in a taxable account. You invest in 1-year bonds with a 5% interest rate, and you continually re-invest the interest payments each year. Your tax rate is 30%. Here are the results:


```
Year: 1, rrsp interest: 50.00, interest from taxable bonds: 50.00, after-tax interest from taxable bonds: 35.00, total nominal rrsp: 1050.00, total nominal taxable: 1035.00, total after-tax rrsp: 735.00, total after-tax taxable: 1035.00
Year: 2, rrsp interest: 52.50, interest from taxable bonds: 51.75, after-tax interest from taxable bonds: 36.22, total nominal rrsp: 1102.50, total nominal taxable: 1071.22, total after-tax rrsp: 771.75, total after-tax taxable: 1071.22
Year: 3, rrsp interest: 55.12, interest from taxable bonds: 53.56, after-tax interest from taxable bonds: 37.49, total nominal rrsp: 1157.62, total nominal taxable: 1108.72, total after-tax rrsp: 810.34, total after-tax taxable: 1108.72
Year: 4, rrsp interest: 57.88, interest from taxable bonds: 55.44, after-tax interest from taxable bonds: 38.81, total nominal rrsp: 1215.51, total nominal taxable: 1147.52, total after-tax rrsp: 850.85, total after-tax taxable: 1147.52
Year: 5, rrsp interest: 60.78, interest from taxable bonds: 57.38, after-tax interest from taxable bonds: 40.16, total nominal rrsp: 1276.28, total nominal taxable: 1187.69, total after-tax rrsp: 893.40, total after-tax taxable: 1187.69
Year: 6, rrsp interest: 63.81, interest from taxable bonds: 59.38, after-tax interest from taxable bonds: 41.57, total nominal rrsp: 1340.10, total nominal taxable: 1229.26, total after-tax rrsp: 938.07, total after-tax taxable: 1229.26
Year: 7, rrsp interest: 67.00, interest from taxable bonds: 61.46, after-tax interest from taxable bonds: 43.02, total nominal rrsp: 1407.10, total nominal taxable: 1272.28, total after-tax rrsp: 984.97, total after-tax taxable: 1272.28
Year: 8, rrsp interest: 70.36, interest from taxable bonds: 63.61, after-tax interest from taxable bonds: 44.53, total nominal rrsp: 1477.46, total nominal taxable: 1316.81, total after-tax rrsp: 1034.22, total after-tax taxable: 1316.81
Year: 9, rrsp interest: 73.87, interest from taxable bonds: 65.84, after-tax interest from taxable bonds: 46.09, total nominal rrsp: 1551.33, total nominal taxable: 1362.90, total after-tax rrsp: 1085.93, total after-tax taxable: 1362.90
Year: 10, rrsp interest: 77.57, interest from taxable bonds: 68.14, after-tax interest from taxable bonds: 47.70, total nominal rrsp: 1628.89, total nominal taxable: 1410.60, total after-tax rrsp: 1140.23, total after-tax taxable: 1410.60
Year: 11, rrsp interest: 81.44, interest from taxable bonds: 70.53, after-tax interest from taxable bonds: 49.37, total nominal rrsp: 1710.34, total nominal taxable: 1459.97, total after-tax rrsp: 1197.24, total after-tax taxable: 1459.97
Year: 12, rrsp interest: 85.52, interest from taxable bonds: 73.00, after-tax interest from taxable bonds: 51.10, total nominal rrsp: 1795.86, total nominal taxable: 1511.07, total after-tax rrsp: 1257.10, total after-tax taxable: 1511.07
Year: 13, rrsp interest: 89.79, interest from taxable bonds: 75.55, after-tax interest from taxable bonds: 52.89, total nominal rrsp: 1885.65, total nominal taxable: 1563.96, total after-tax rrsp: 1319.95, total after-tax taxable: 1563.96
Year: 14, rrsp interest: 94.28, interest from taxable bonds: 78.20, after-tax interest from taxable bonds: 54.74, total nominal rrsp: 1979.93, total nominal taxable: 1618.69, total after-tax rrsp: 1385.95, total after-tax taxable: 1618.69
Year: 15, rrsp interest: 99.00, interest from taxable bonds: 80.93, after-tax interest from taxable bonds: 56.65, total nominal rrsp: 2078.93, total nominal taxable: 1675.35, total after-tax rrsp: 1455.25, total after-tax taxable: 1675.35
Year: 16, rrsp interest: 103.95, interest from taxable bonds: 83.77, after-tax interest from taxable bonds: 58.64, total nominal rrsp: 2182.87, total nominal taxable: 1733.99, total after-tax rrsp: 1528.01, total after-tax taxable: 1733.99
Year: 17, rrsp interest: 109.14, interest from taxable bonds: 86.70, after-tax interest from taxable bonds: 60.69, total nominal rrsp: 2292.02, total nominal taxable: 1794.68, total after-tax rrsp: 1604.41, total after-tax taxable: 1794.68
Year: 18, rrsp interest: 114.60, interest from taxable bonds: 89.73, after-tax interest from taxable bonds: 62.81, total nominal rrsp: 2406.62, total nominal taxable: 1857.49, total after-tax rrsp: 1684.63, total after-tax taxable: 1857.49
Year: 19, rrsp interest: 120.33, interest from taxable bonds: 92.87, after-tax interest from taxable bonds: 65.01, total nominal rrsp: 2526.95, total nominal taxable: 1922.50, total after-tax rrsp: 1768.87, total after-tax taxable: 1922.50
Year: 20, rrsp interest: 126.35, interest from taxable bonds: 96.13, after-tax interest from taxable bonds: 67.29, total nominal rrsp: 2653.30, total nominal taxable: 1989.79, total after-tax rrsp: 1857.31, total after-tax taxable: 1989.79
Year: 21, rrsp interest: 132.66, interest from taxable bonds: 99.49, after-tax interest from taxable bonds: 69.64, total nominal rrsp: 2785.96, total nominal taxable: 2059.43, total after-tax rrsp: 1950.17, total after-tax taxable: 2059.43
Year: 22, rrsp interest: 139.30, interest from taxable bonds: 102.97, after-tax interest from taxable bonds: 72.08, total nominal rrsp: 2925.26, total nominal taxable: 2131.51, total after-tax rrsp: 2047.68, total after-tax taxable: 2131.51
Year: 23, rrsp interest: 146.26, interest from taxable bonds: 106.58, after-tax interest from taxable bonds: 74.60, total nominal rrsp: 3071.52, total nominal taxable: 2206.11, total after-tax rrsp: 2150.07, total after-tax taxable: 2206.11
Year: 24, rrsp interest: 153.58, interest from taxable bonds: 110.31, after-tax interest from taxable bonds: 77.21, total nominal rrsp: 3225.10, total nominal taxable: 2283.33, total after-tax rrsp: 2257.57, total after-tax taxable: 2283.33
Year: 25, rrsp interest: 161.25, interest from taxable bonds: 114.17, after-tax interest from taxable bonds: 79.92, total nominal rrsp: 3386.35, total nominal taxable: 2363.24, total after-tax rrsp: 2370.45, total after-tax taxable: 2363.24
Year: 26, rrsp interest: 169.32, interest from taxable bonds: 118.16, after-tax interest from taxable bonds: 82.71, total nominal rrsp: 3555.67, total nominal taxable: 2445.96, total after-tax rrsp: 2488.97, total after-tax taxable: 2445.96
Year: 27, rrsp interest: 177.78, interest from taxable bonds: 122.30, after-tax interest from taxable bonds: 85.61, total nominal rrsp: 3733.46, total nominal taxable: 2531.57, total after-tax rrsp: 2613.42, total after-tax taxable: 2531.57
Year: 28, rrsp interest: 186.67, interest from taxable bonds: 126.58, after-tax interest from taxable bonds: 88.60, total nominal rrsp: 3920.13, total nominal taxable: 2620.17, total after-tax rrsp: 2744.09, total after-tax taxable: 2620.17
Year: 29, rrsp interest: 196.01, interest from taxable bonds: 131.01, after-tax interest from taxable bonds: 91.71, total nominal rrsp: 4116.14, total nominal taxable: 2711.88, total after-tax rrsp: 2881.29, total after-tax taxable: 2711.88
Year: 30, rrsp interest: 205.81, interest from taxable bonds: 135.59, after-tax interest from taxable bonds: 94.92, total nominal rrsp: 4321.94, total nominal taxable: 2806.79, total after-tax rrsp: 3025.36, total after-tax taxable: 2806.79
```
In your taxable account, you have to pay tax on the interest payment immediately. In the first year the bond pays $50, but you pay 30% tax and so you only end up with $35, bringing your balance to $1035 which can be invested in another 1 year bond. In your RRSP, you don't pay tax on that $50 (yet), so you can re-invest it.

Initially you can see that the after-tax value of the RRSP is much less than the taxable account (again, because I didn't correct for it in the beginning), but by the end the RRSP has a higher after-tax value.


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## Dave (Apr 5, 2009)

slacker said:


> One more clarification. RRSP is not locked in, and there is no penalty for withdrawal.
> 
> RRSP offers you the chance to skip out on taxes that you owe to the government for a long long time, decades if you wish. The only catch is that, you'll have to pay that tax sometime later, at a time of your choosing.
> 
> ...


Slacker, you had the most convincing argument. I hit the highest tax bracket this year so it makes sense to throw money in the RRSP. Future income will be tax-sheltered in a corporation, so I should not be in the highest bracket again, unless I decide to buy a house or do something major in an undeterminate future. Then I could always cash out the RRSP.

TFSA is maxed and it is the best thing, I never had any dobuts about it. 

Dave


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## steve41 (Apr 18, 2009)

> Your tax rate is 30%.


 There is no such thing as a tax rate.... there is only the T1 itself (income tax algorithm). When you make these determinations, (RSP vs nonreg vs TFSA) or pay down loan vs not, or take early vs late CPP..... you are badly approximating. This kind of math (tax accurate) is not well-suited for spreadsheeting.


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## Donny (Dec 14, 2011)

steve41 said:


> There is no such thing as a tax rate.... there is only the T1 itself (income tax algorithm). When you make these determinations, (RSP vs nonreg vs TFSA) or pay down loan vs not, or take early vs late CPP..... you are badly approximating. This kind of math (tax accurate) is not well-suited for spreadsheeting.


It's a simplification. Consider it short hand for "your marginal tax rate is x% and the amount of money you will make or not make from this example will not change your marginal tax rate"

I don't think that simplification changes the result of the data I posted, which is that the tax-free compounding is an advantage of an RRSP.


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## Charlie (May 20, 2011)

I think slacker summed it up nicely.

With an RRSP you get a 'loan' of the tax you would otherwise have paid.

If you withdraw at a lower bracket you win on all counts
If you withdraw at a similar bracket you get an interest free loan over decades
and even if you withdraw at a higher bracket the deferral over decades usually makes the added tax well worth while. (imagine if someone loaned you a dollar today -- and asked that you pay back $1.50 in forty or fifty yrs. Not necessarily a bad deal -- you get the earnings (also tax deferred) over that timeframe). 

There are other benefits -- HBP/LLP/structured savings/creditor protection/flexibility/avoidance of income spikes due to investments/etc.


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## MoneyGal (Apr 24, 2009)

Plus the value of a dollar paid in tax in 30 years is much less than a dollar paid in tax today. 

Even if they're "the same amount" - a dollar is a dollar is a dollar [which is essentially what the spreadsheet says] - people rationally want to put off paying a dollar due as long as possible. And that's what RRSPs allow you to do.


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## steve41 (Apr 18, 2009)

Further to MG's comment....

You will notice an insertion in every plan I post. It sits at the top of the Retirement Projection report thusly.....

"Tax (total/PV)= $160K/$75K"

What this represents is that the program has totalled the column of tax pmts in 2 ways. The first number is the actual total of the tax paid column and the second number is the present value (PV) of that same tax column.

In every case, the most efficient (highest after tax plan) will be the plan where the 2nd number (PV tax) is lowest..... not the 1st number (total tax)


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## slacker (Mar 8, 2010)

At the risk of detracting from what I said before...

The government wants that tax back sometime later, but for doing a favour to you, the government want a slice of the profits you had from investing base on the tax deferral.

In other words, if you made money from the government's generous offer of tax deferral, the government wants a slice. It's still a good deal, but they always want their share.


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## steve41 (Apr 18, 2009)

Actually, the RRSP is essentially tax neutral. If you compare an RRSP strategy vs a TFSA strategy, the results are virtually the same. The caveat being that the strategy is a textbook.... working stiff, saving, retiring, and drawing down their savings in retirement.


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## Sampson (Apr 3, 2009)

remember this thread well.. MG and steve agreeing completely, at least one part of the model/planning.


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## Saniokca (Sep 5, 2009)

Steve,

I haven't given this much thought yet (i.e. didn't look at the math). It seems to me however that RRSP will mainly be advantageous for bonds/GICs. On stocks you pay taxes on 50% of the cap gains (at what rate? marginal?) and 15% tax on dividends (am this right?). When you withdraw, you will pay your marginal rate on that income if you invest inside RRSP wouldn't you?


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## 0xCC (Jan 5, 2012)

You aren't right on the tax rates for dividends. I think that is probably the US tax rate but I could be wrong on that. Capital gains are taxed at 50% of your marginal rate if realized outside of a registered account. I use www.taxtips.ca to remind me of thetax rates for my situation. Which account should hold which investments is really a personal choice and depend on your circumstances and objectives.


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## Financial Cents (Jul 22, 2010)

jamesbe said:


> People do this? IE: Put in $1000 this year to get a "tax break" then take it out to get the money back???


I really hope not but who knows.


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## MrMatt (Dec 21, 2011)

Financial Cents said:


> I really hope not but who knows.


Yes there really are people who do. The sad part there is they blow the refund, and they'll even structure their withdrawals the next year to avoid withholding tax. It's shocking how carefully they implement a moronic strategy.

There are also people who don't contribute to matching pension plans at work, even unlocked RRSP plans because they think it's all a bank scam.

It's sad when there are those who put the minimum to get the company match, then withdraw it, but at least they're taking advantage of the companies "free money".


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## steve41 (Apr 18, 2009)

Saniokca said:


> Steve,
> 
> I haven't given this much thought yet (i.e. didn't look at the math). It seems to me however that RRSP will mainly be advantageous for bonds/GICs. On stocks you pay taxes on 50% of the cap gains (at what rate? marginal?) and 15% tax on dividends (am this right?). When you withdraw, you will pay your marginal rate on that income if you invest inside RRSP wouldn't you?


Three things are at work here....

1. the time value of money effect.... would you rather pay $1000 in tax now, or $2000 in tax 10 years from now? Tax has to be looked at in PV terms.

2. in retirement, there are various age credits, the pension tax credit, etc

3. the effect of the indexing of the income tax brackets. Bracket Creep is dead, remember.

The effect of this last item means that, while tax on $50k is $8.7k now, in 50 years, tax on 50K will be just $4.1K. (For an inflation rate of 2%, BC tax rates)


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## lb71 (Apr 3, 2009)

slacker said:


> RRSP is not locked in, and there is no penalty for withdrawal.


But you do lose that contribution room.


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## CanadianCapitalist (Mar 31, 2009)

Saniokca said:


> Steve,
> 
> I haven't given this much thought yet (i.e. didn't look at the math). It seems to me however that RRSP will mainly be advantageous for bonds/GICs. On stocks you pay taxes on 50% of the cap gains (at what rate? marginal?) and 15% tax on dividends (am this right?). When you withdraw, you will pay your marginal rate on that income if you invest inside RRSP wouldn't you?


Not true. If you have RRSP room, keeping stocks within it will almost always come out ahead. That's because in a taxable account, you are paying taxes every year (dividends and/or capital gains) whereas you defer taxes inside a RRSP allowing your investment to truly compound.


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## lb71 (Apr 3, 2009)

CanadianCapitalist said:


> Not true. If you have RRSP room, keeping stocks within it will almost always come out ahead. That's because in a taxable account, you are paying taxes every year (dividends and/or capital gains) whereas you defer taxes inside a RRSP allowing your investment to truly compound.


It would depend on the growth of the stocks, your level of trading and the expected investment horizon. If the stock is a low dividend high growth stock, you may be better off holding outside the RSP. If you do a lot of trading, then an RSP would defer the capital gains hit. 

If you are strickly invested in equities, then yes, do put some into your RSP. But if you have a mix of fixed income and equities, generally you are better allocating your fixed income in your RSP first.


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## Donny (Dec 14, 2011)

lb71 said:


> It would depend on the growth of the stocks, your level of trading and the expected investment horizon. If the stock is a low dividend high growth stock, you may be better off holding outside the RSP. If you do a lot of trading, then an RSP would defer the capital gains hit.


I can't think of a situation where it would be better to hold it outside the RRSP, could you give an example?

I tried it out comparing $1000 of pre-tax income in an RRSP vs a taxable account.
Assuming you face a 30% marginal tax rate, you buy a stock that gives out no dividends and grows 50% over some period of years, then you withdraw your money and again face a 30% tax rate on withdrawal:

RRSP: $1000 before-tax money gets invested, grows 50% to $1500, you withdraw it and pay 30% leaving you with $1050 after tax which you can then spend.

Taxable: You have $1000 before-tax money, you pay 30% tax leaving you with $700 to invest. It grows at 50% to $1050, at which point you want to spend it. You have $350 of capital gains, you pay 30% on half that amount since it's capital gains and you're left with only $997.50 after tax to spend.

Even in this situation with no dividends and all capital gains, putting it in the RRSP is best (again, assuming no benefit/penalty from changes in tax rate on contribution vs withdrawal). Any extra trading just makes it even more favorable to the RRSP.


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## warp (Sep 4, 2010)

Heres my simple thoughts:

1) You should contribute to your RRSP about the dollar amount that will lower your "taxable income" to the lowest tax rate.

2) As a general rule of thumb, not exact, anyone making less than about $40K a year would be better off using the TFSA, rather than contributing to an RRSP. High earners should contribute to RRSP's , then also use the TFSA 

3) Any RRSP money should be left IN the RRSP to allow for compounding, and should be used like a savings account only as a last resort.
Any young person will be glad they have a nice RRSP nest egg, as the years surely will go by.

Just my 2 cents.


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