I'd be careful how you word it [w.r.t whatever sales acts you have wherever you are]An advertised "discount" or "reduced price" that is the actual usual selling price in the UK is dodgy for example.
They do save money if they pay by the semester, or to state it another way, they pay more if they want to make several smaller payments.
E.g note you've called it a 7% discount that you "offered" in one post that was taken up within a couple of years by everyone - that suggests different people were paying 2 rates, one of which they thought was a discount, no? The next post suggests it's wasn't a discount at all, because it's what you would normally charge and suggests you'd add 10%. The next says you don't use the word discount at all - but yeah, your posts aren't your policy - my point is, if you're going to have a policy be wary of the fact that what you say in that does matter - at least in most places - even if it looks mathematically like you're "stating it another way" - from the pov of the usual consumer legislation, how you state it does matter.
PS Jeremy, getting back to your original question, if it's just one mom asking for a discount, then that would be actual money you would lose. There's not much advantage to you in this case. But if you ever decide you want to save yourself some bookkeeping time, make lump payments the standard (however much you need to earn), and set your monthly payments to total a little more than the lump sum. Then you don't lose any money, and you can spend more time teaching and less time messing with checks.