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It depends on the provisions for coordination of benefits. Some do, some don't.
Within every health insurance policy there are "free" benefits, such as preventive care. In addition, most policies - not all - offer benefits such as a copay for office visits and even copays for precriptions benefits. Let's refer to these benefits a PRE-DEDUCTIBLE benefits. Other than whatever pre-deductible benefits are included on your policy YOU are responsible for all other medical expenses until you have spent the amount equal to your deductible. If you have a $1,500 deductible, other than your pre-deductible benefits, you would be responsible for the first $1,500 in medical expenses each calendar year. After that, the carrier will begin paying their share.
That is if the secondary does not have a clause in it that "they will not duplicate benefits" If so they will not always pay the difference. They will figure out the amount they would normally pay, subtract what the primary pays from that amount and pay the difference (which with mine is little to nothing and I end up paying the balance of the bill) Nothing really happens, one is the primary and the other is the secondary insurance for the patient. Primary insurance will pay up to 80% of allowed charges if the deductible is met, and the secondary insurance will pay the remaining 20% of the claim, again, if the deductible for the year has been met.
After you have received the Explanation Of Benefits (EOB) from your primary carrier if there is coordination of benefits. If the secondary insurance is an indemnity you do not need to wait.
its called the deductible. ask an insurance company about it.
Generally, the premiums are not deductible, and benefits would not be taxable income.
Deductible
it protects against catastrophic losses yet avoids administrative burdens associated with smaller claims below the deductible amount.
Whether for health or automobile insurance, these plans require you to pay a greater part of the cost of insured services. The benefit is that your premium is lower--with auto insurance, frequently increasing your deductible can reduce your premium by more than the deductible (i.e., if you raise your comprehensive from $250 to $100, you would save $160 a year). There is also a secondary benefit in that you will make fewer claims which will reduce the likelihood of your policy being cancelled or having your premiums go up in the future.
I'm not sure what you mean by a "secondary" insurance.
Secondary.
It's tax deductible, guaranteed issue and it attracts a better class of worker.