If you are calculating for a loan, you need to follow the frequency laid out in the loan paperwork.

e.g.1 - I have had two auto loans - they compounded daily.

e.g.2 - I have dealt with two separate CUs for my mortgage, they compound monthly.

If you are calculating for your own savings rate etc - it's all assumptions and approximations. Generally, for stock market, people like to express returns as CAGR, which is a geometric mean of annual growth over a period of time.

There is no intrinsic harm if you like to use a continuous compounding for this purpose instead of annual CAGR. Indeed, I find the calculations to be far easier and intuitive (natural log and e^x is a lot simpler and intuitive than the ugly looking CAGR formula) with continuous compounding assumptions. If you like daily, all power to you and calculate away. I find daily to be even uglier than annual, but you do it if you like it.

One issue that can happen if you choose non-conventional compounding frequency is that you won't be able to easily compare your numbers against numbers from bankrate - for example, because they will follow a different convention comparing theirs to yours would be apples to oranges. So it is generally more convenient to follow the widely used convention like CAGR when you are dealing with the stock market returns.