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If we have an annual rate of return of 7% for our stock investment, how much is the monthly rate?

First of all, why might we want to use monthly rate: that's because we may do monthly contribution of $300 to the account, so we need to calculate it month by month.

I have seen articles that talk about just to divide the annual rate by 12.

However, let's say, we look at $1000.

Assume we don't have money to contribute for the month, for simplicity of calculation.

Divide by 12 method:

$1000 * 7 / 100 / 12 = 0.583333 %

using this method, we have $1072.2901 at the end of 12 months. (please see spreadsheet at the end of question).

30 years later by the same calculation method in the spreadsheet, it is $8116.4975

Exponential method:

rate is really:

(1 + 0.07) ** (1 / 12) - 1 = 0.5654145387405274 %

(the ** above means "to the power of")

using this method, we have $1070.0000 at the end of 12 months. (please see spreadsheet at the end of question).

30 years later by the same calculation method in the spreadsheet, it is $7612.2550

What it really is, $1000 at 7% for 30 years:

1000 * (1.07) ** 30 = 7612.255042662042

so it looks like we really should use method 2? The bank giving us the rate of 7% / 12 = 0.583333 % would be a "nominal value" for us to divide by 12, if the compounding is by monthly, and everybody does it by dividing by 12. But if it is our investment calculations, then it seems it really should be by method 2?

By Method 1:

By Method 2:

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  • (1 + 0.07) ** (1 / 12) - 1 = 0.5654145387405274 % is the same as =RRI(12,1000,1070). Multiply that by 12 to get the CAGR of 6.785%. – RonJohn Feb 13 at 15:44
  • I'd then do =1000*(1+0.5654%)^(30*12) and get the number 7612.255. (If you try my formula, the numbers will be slightly off due to formatting -- Excel only displays 5 digits). – RonJohn Feb 13 at 15:49
  • the idea of using the term RRI is quite good... so when people state RRI, people who don't know what RRI is dare not say a word. If I just present some math calculation, then it can be like 10 people and there are 2 or 3 different opinions – nonopolarity Feb 13 at 17:07
  • RRI means, I think, Rate of Return on Investment. – RonJohn Feb 13 at 17:30
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Rates for loans and fixed income deposits (savings accounts, bonds) are typically quoted as an annualized rate without compounding, so when you see a loan at 12% interest, it's really a loan at 1% monthly. Quoting that way makes different compounding periods easily comparable and easier for consumers to understand the actual rate used without having to go into the complex math of compounding.

But that's not what you're looking at. You're looking at how much you are earning monthly taking compounding into consideration, so taking your annual gain to the 1/12 exponent is appropriate, meaning that you'll get the same return compounding the monthly return over 30 years as the annual return (1.56541453874 ^ (30*12) == (1.07)^30).

Or, put another way, what's the monthly growth you'll need to end up with a 7% return at the end of one year? You've shown that method 2 is the correct way to calculate that.

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I would go for the simpler method when doing the calculations. I base that a key assumption you have made in your question:

  • annual rate of return of 7% for our stock investment.

That is not guaranteed. It is in fact the long term average. You will have years where it is in the double digits, and years where it is negative. That is even more true if you try to break it down by month, during the 12 months there will be weeks or months where the value goes down. Think of the crash in the spring of 2020, but the S&P 500 still was up more than 15% for the year.

When looking at investments that will stretch out for decades you will not need to break it down by month, annual numbers work just as well as a guess.

If you are looking at an investment that will only last a few months then annual numbers have no meaning.

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    I stated in my question why I need to do it by months. As to: we cannot predict the market anyway: we cannot predict the market, but at least we can do the calculation correctly. If we can't predict the market and we do inaccurate calculations, it only makes it worse. It simply is to do some correct calculation of if it is 7% increase in a year, then how much does that increase in a month? – nonopolarity Feb 13 at 17:05

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