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
rate is really:
(1 + 0.07) ** (1 / 12) - 1 = 0.5654145387405274 %
** 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: