That much-appreciated limited period of time in which penalties are not imposed even if you are late—for whatever (insurance, class, appointment, or any kind of bill)—is called grace period. Very apt. Although undeserved, it is given out of consideration for inability.
Grace periods come with different time frames—some short, some long—but the important thing is: as long as you make it during this time, you are free from any obligation or punishment.
In sum, you or your payments are not considered late.
In the university where I teach, grace period is 15 minutes after the start of the official class hour. Beyond that, students are no longer accepted into the classroom.
Their penalty translates to missed opportunity (lecture, quiz, project, discussion, etc.) that leads to lowered grade.
A grace period is exactly that—it is grace; it is given to anyone who, even if late, has the same privileges as those who are on time.
On earth, our grace period within which to accept “the Way, the Truth, and the Life” is our lifespan. We are given our whole lifetime to say “aye” or "nay” to Jesus.
Many people take their own sweet time, saying life has to be enjoyed first. The trouble is, tomorrow may not come; our life could end tonight or anytime. Beyond that, we will stand in judgment.
Alas, the grace period granted us cannot be taken for granted.
“Yet you do not know what tomorrow will bring. What is your life? For you are a mist that appears for a little time and then vanishes.” James 4:14 (ESV)