"The less notices clients receive, the better. "
Even if you calculate the amounts correctly, the client is going to get a notice that interest and penalty have been assessed. Further down, it might or might not be obvious that the amount assessed was paid and there is no balance due. So as they say in Arkansas, that dog don't hunt.
There are different rules on calculating interest, depending on whether it's for a corporation or individual, and whether there is just additional tax, or it comes with additional credits. You need a transcript to figure out the assessment date, and the payment dates.
This falls into the category of Socialist Software. Charge 99.8% of users for a feature that 0.2% might use, and there's no guarantee of a correct answer. For the easy cases, there are websites that already do that. Mark me down as a NO.