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Email this12:47 pm
April 6, 2013
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Jon said
Actually, what Norman suggesting seems like a important skills to have for calculating return on investment. It will be a good idea if Norman, in his free time, can try to teach and explain much more in detail to other members, as it is useful and will help clear the air in here even better.
The average compounded annual growth rate (CAGR) is an average return over the time period. It is the percentage change each year (calcuated against the balance at the start of each year) that would give the same ending balance over the same n years. The formula is
CAGR = n√ end / start - 1
Double money in 10 years means
CAGR = 10√$2,000/$1,000 - 1
= 10√2 - 1
= 0.07177
= 7.177% per year
There is a shortcut when one has the individual yearly returns, like with an escalating GIC. For example, the escalating five-year compounding GIC with 1%, 2%, 3%, 4%, and 5% annual returns that Oscar mentioned:
CAGR = n√ end / start - 1
= 5√$1000(1 + 0.01)(1 + 0.02)(1 + 0.03)(1 + 0.04)(1 + 0.05) / $1000 - 1
= 5√(1 + 0.01)(1 + 0.02)(1 + 0.03)(1 + 0.04)(1 + 0.05) - 1
Now, 5√(1 + 0.01)(1 + 0.02)(1 + 0.03)(1 + 0.04)(1 + 0.05) is the fifth root of five numbers multiplied together. That is, by definition, the geometric mean of the five numbers. If one has a spreadsheet, that term can be replaced with the built-in @GEOMEAN function:
= @GEOMEAN(1 + 0.01, 1 + 0.02, 1 + 0.03, 1 + 0.04, 1 + 0.05) - 1
= 1.02990 - 1
= 0.02990
= 2.990% per year
That supports Oscar's finding that the escalating GIC is not quite as good as a regular 3% five-year compounding GIC. That's because the quoted rate for an annual compounding GIC is the same as its CAGR. 
1:08 pm
December 17, 2016
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Oscar said
They also have a 5 year escalator at 1 , 2 , 3 , 4 , and 5% and averages 3%/annum when offered this way to a guy doing math on his fingers like myself but it yields less than a 5yr@3%/annum GIC. So the math does make a difference $$ and I'm glad someone took the time to demonstrate it although it did fly right over me
- The 5 year escalator GIC at 1 , 2 , 3 , 4 , and 5% equals an average ROI of 3.17% per year, at maturity.
- The 5-year 3.00% per annum GIC equals an average ROI of 3.19% per year, at maturity.
So the math does make a difference $$ ... using plain old simple arithmetic one can say balderdash to that claim UNLESS 10¢ on a $100 over 5 years is considered big coin.
2:47 pm
April 6, 2013
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Oscar said
…
They also have a 5 year escalator at 1 , 2 , 3 , 4 , and 5% and averages 3%/annum when offered this way to a guy doing math on his fingers like myself but it yields less than a 5yr@3%/annum GIC. So the math does make a difference $$ …
I think a classical example of the issue with calculating the arithmetic average of the yearly returns is when the yearly returns are something like -50% and +100%. The arithmetic average is
(-50% +100%) / 2 = +25% per year
In reality, losing 50% of the original $1,000 one year and then growing the $500 remaining by 100% next year gives just the original $1,000. 
The CAGR better reflects the result:
CAGR = @GEOMEAN(1 - 0.50, 1 + 1.00) - 1
= 1 - 1
= 0% per year
5:23 am
February 20, 2018
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any reason not to do the rap 5yr 3.62 compounded 3.89? any of you with cash wouldn't do why?
6:46 am
April 6, 2013
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I wouldn't because there are better rates still available.
Loonie mentioned DUCA offering 5 years at a higher 3.75% and Ganaraska Financial offering a shorter 4 years at a higher 4%.
6:42 pm
October 21, 2013
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It is precisely for answering questions like this that I find my method of calculation useful. See my post above #4.
If you go with Rapport, at the end of five years, you will have earned $19.45 per $100 invested.
Using DUCA, you would have $20.22 at the end of five years.
At Ganaraska, at the end of FOUR years, you would have $16.99 . In order to know what you'd have in five years, you'd have to speculate on what you might get in that fifth year. If we assume it's at least 3.25% (the going best rate for one year GIC), then you would have $20.79 after five years.
But, of course, we don't know what that extra year would bring. You can't really compare the returns for different terms unless you look at it in terms of how much you get per year - in my opinion at least.
Thus,
Rapport earns 19.45 / 5 = 3.89 average annually;
DUCA earns 20.22 / 5 = 4.04 average annually;
and Ganaraska will earn 16.99 / 4 = 4.25 average annually.
No doubt Norman will have another way of calculating it, but I imagine the results will point in the same direction.
If you want to invest for five years, you should go with DUCA.
I can only think of one situation where Rapport might be better. If they allow annual interest payout, and if you choose this, and if you use it to pay down a debt (which typically will have a higher interest rate), then you might be better off with Rapport because the first year rate is high and wil give you more up-front interest with which to reduce your debt and consequent interest owed. You would need to do the math for your particular situation to see if this would be beneficial.
If you can be content with four years and taking pot luck on the fifth, you would be better with Ganaraska, if it is available where you live. But I must stress that none of these rates will likely be available much longer.
Sometimes there is another round of rate specials starting in April, as the FIs build up their reserves for the Spring housing, reno, and car-buying market, but not always.
1:57 pm
February 20, 2018
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it appears rap 5yr was top of market for now anyone 3.65+
9:39 pm
February 20, 2018
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Apparently they had 1yr@3.1 n 18mth@3.25 as recently as last week
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