It's actually pretty simple:
The purpose of life is to propagate life.
You come to the same conclusion from any angle, after asking why enough times, like an annoying child. Take daygame for example:
Why am I daygaming? I want more sex.
Why do I want more sex? Because it feels good.
Why does it feel good? Because it's supposed to help propagate life.
Now try work:
Why do I work? Because it gives me money.
Why do I need money? Because I want water, food, shelter, etc.
Why do I want those things? Because they're supposed to help propagate life.
Of course, the devil is in the details, such as the best ways to propagate life. Consider this hypothetical example, in place of the first line in the last example:
Why did I steal instead of work? Because I believe it's the best way to get money (regardless if it actually is or not).
The question then becomes what are the best ways to propagate life. I won't answer that here, other than to say: science!