Re: Maybe this bit of income equalization...
I should add a caveat to what I said, that relates to the question of payouts exceeding contributions. I know, just when it seemed safe to look at the forums. But -
It is of course possible to operate a system with no interest or investment return at all. It's equivalent to stuffing your money into an old tomato can and burying it in the back yard until retirement. In that case, the total payout obviously equals the total contribution, and the annual payout R would just be the annual contribution C times the ratio of the contribution period to the payout period.
It would still be a contributory system, which if I can recall that far back was my original point such as it was, just not a particularly attractive one. No pension system works like that for the obvious reason that providing the defined benefit is more expensive to the provider. As we've seen, even a low rate of return on the order of a couple percent will double the payout for a given rate of contribution due to the long time period of investment.
I'll back away from the keyboard now and go outside for some fresh air.