On monthly vs daily calculations - you should stick to monthly calculations when instalments are paid monthly otherwise, as you say, it gets messy.
Daily calculations should only be applied on variations, and you'd typically offset this from the last regular transaction.
I think you've got a problem with the calculation you're using. The advertised rate needs to be the annual effective rate of interest, so unfortunately determining the monthly rate for compound interest is not as simple as "annual rate / 12".
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