Plain version: most people never pay for Part A, because they or a spouse paid Medicare taxes while working. Medicare also rewards signing up on time: wait without a good reason and you pay more, sometimes for life.
Part A premium by Social Security work credits (quarters of coverage):
40 or more credits: premium-free Part A.
30 through 39 credits: reduced monthly premium. A person can also use a spouse's record for the reduced premium if married for at least the past year to a worker with 30 or more.
0 through 29 credits: full monthly premium. A person who buys Part A this way must also be entitled to or enrolled in Part B. Too few credits raises the cost; it does not shut the person out.
Part A late penalty (for people who must buy Part A): the premium goes up 10%, no matter how long the delay, and the higher premium is paid for twice the number of full 12-month periods the person could have enrolled but did not. Example: three years late means 10% more for six years.
Part B late penalty: the standard Part B premium goes up 10% for each full 12 months the person could have had Part B but did not. Partial years do not count, and the penalty generally lasts as long as the person has Part B. Example: 30 months late contains two full 12-month periods, so the penalty is 20%.