Even the poor Indian child who earns $2 per day sewing clothes... if she can survive on $2 a day, she can survive on $1.98 a day, and invest 1% of her income. That % put away builds exponentially, and always ends up significant if you only have the discipline to stick to the plan.
It would work (provided there is no limitation of another kind) only if lifespan were
infinite (this is the crucial premise your assumption lacks)...