The answer to this question depends on what your financial worst case scenario really is.
If you are single without dependants and you work for a living, then the worst thing that could happen is that you become completely unable to work. In this case the most important thing to insure is your income.
If you are single with dependants and you work for a living, then its still the case that the worst thing that could happen is that you become completely unable to work. But a very close second is that you die before your dependants are able to make their own way in the world. You need to insure your income and your life as the highest priority.
If you are married / whatever with a partner, and no dependants, then you aren’t in too bad a position. The worst case would be that you both lost your ability to provide an income, so you need income insurance, but it might not need to be as generous (since the other partner should still have an income).
If you are married with dependants, then the worst possible scenario is that you both die before your dependants are financially secure. You need life insurance first, with income insurance second for all the reasons above.
If you have a secure independent income with no access to capital (like you have an annuity or similar) and you have dependants, then you need life insurance. Unfortunately, if you are in this position you are likely to be older and not get a good deal on life insurance. Your best bet might be to save as much as possible and hope that you live long enough.
Of course, I’ve painted broad generalisations here. What you should really do is take an honest look at the risks and outcomes of all bad financial situations and plan accordingly. The safety net of an emergency fund will help in almost every situation.
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