As Dorkus said, it can be forget about it money. (it pretty much needs to be if you put it in a retirement account.) However if you put it in a taxable account, then you can always access it, but you'll have to pay taxes on the gains when you sell. You'll still have to pay taxes on your CD gains (even though they may be at different rates), but look at it this way, you'll only be paying taxes when you make money, so taxes, while you hate them, are a good sign.
Also, you'll be getting dividends which will be taxed lower than your gains. Obviously you'll want to re-invest them, but if you feel you need access to money, you can just turn the dividends to deposit into your bank account. That might stem the tide to where you won't need to "withdraw" your funds, and whenever you feel like you don't need that check coming in, just simply set the dividends to re-invest again.
If you never know when you'll need the money, I'd rather have my money in an index fund, as if you feel you need money, it'll only take like a week to get the funds transferred. As opposed to if you need it from a CD, you'll have to wait until the end of the month, at the EARLIEST, depending on how good of a ladder you set up.
However with all that being said, if you're able to consistently save 3k in 2 months, you should be able to put this money away, even in a taxable account, and make it be "forget about it" money... or lets say "forget about it money... that I can access if I ever truly need to." I hope that all makes sense, I tend to ramble.
As for the daily interest amount, I know they calculate via a daily balance rate. It's so you can't just transfer 30k to your savings account on the 30th of every month, and then take it back out on the 1st again, after getting lots of interest. You have to keep your money there for the entire month, to actually get the total interest on every dollar. I just don't know that formula they use. (Probably something like annual rate divided by 12, then divided by the days of the month, times the balance of the day.) If you move a big chunk of change from that account, you'll see that number change, and then that will be the number they use for the remaining days, until the balance changes. I use 360, but they don't list the amount earned that day, just a running total of interest earned... maybe it's time to make a suggestion! Thanks for letting me know where that came from!