I am reading AAA Term Life Insurance offer. I am wondering that the
rate will stay inside the same group until the end of the insurance
(80 years old) or will jump to a different group when you are older
Term life insurance has options, besides the amount of insurance. The most important is the length of the term. It isn't unusual to see terms of 5, 10, or 20 years.
Another important option is does the policy have a level premium? If it does, then the amount you pay each year doesn't change during the term of the policy. That does mean that you overpay in the early years to underpay in the later years. If you keep it the entire term to works out in the end, but if you drop the policy early you spent more than you need to. Don't get me wrong, a term that meets your needs is a good thing.
Some policies will require you to take a physical exam, but that depends on the size of the policy and their rules.
For example, if I am in the 55-59 group right now, a few years later,
I will use the rate for 60-64, 65-69,...?
Ignoring health for a moment. The initial rate will depend on the size of the policy, the length of the term, and which age group you are in. The length of the term determines which group you will be in at the end. They will use the starting and ending groups to determine how to craft the level premium.
Of course when the term ends if you still need/want insurance you will be in another age group, so it might be much more expensive to get another policy. In addition your health might not be as good, which can move you to a more expensive category.
Saying I will just get the longest term they offer can seem to make sense, but it can be costly. You will overpay in the first half of the term. Many people buying a policy when they have their first kid, discover that by the time they have their last child they might need a different amount, so locking in a policy for decades might not be the best.
They didn't mention the premium. That means no money back at the end?
Those are two different things. The premium is what you pay each month/year.
Some policies do have a cash value, and can give it to you at the end of the term.
If the cash value at the end is what is important to you, then you may be looking for a non-term policy. Those policies are a mix of insurance and investing. They generally are the worst of both, and are completely different than term policy.