So the interest is quoted as 4% calculated daily, and compounded semi-annually.
If you simply dropped $100 into this account on Jan 1 and did nothing else, then the only activity you would see would be a deposit of $2.00 on June 30, and a further deposit of $2.04 on Dec 31. The only time that the "calculated daily" takes effect is when there are cash flows into or out of the account during the year.
A rate of 4% a year is the equivalent of 4/365 or 0.010959% per day.
So as cash flowed into and out of the account, each day someone would calculate how much interest the balance in the account for that day had earned for that day. The amount of this interest would be recorded somewhere, but would not appear anywhere in the account balance.
Since the interest is compounded semi-annually, on June 30 and Dec 31 the accumulated total of this interest would be credited to the account and would then begin to accumulate interest-on-interest, i.e. "compound"
I can recall, in the dim distant days of my youth, where interest was calculated (possibly on an abacus) compounded semi-annually based on the minimum semi-annual balance!