It is a miracle! Did you know if you save one penny today and invest it at 4% that in 1000 years you will have 2 thousand trillion dollars! It is true!
Also, you'll be dead and probably someone will have stolen it from your retirement account by then, but it is still a miracle!
Once when I was on some conference panel on retirement, pushing the crazy idea that we need more Social Security, I was trying to push the point that relying on 401k plans for retirement essentially requires a best case scenario:
1) people have stable employment from young adulthood until retirement
2) they start saving immediately and constantly in a nontrivial fashion for retirement
of course those young people also:
1) have low wage entry level jobs
2) have to pay back student loans
3) have to pay rent and eat
4) are "supposed" to get married and have bebbies (and, you know, we aren't peacocks, but the mating market requires a bit of expensive peacocking)
5) have to save for college for their bebbies
6) have to save for a downpayment for a house
The miracle of compound interest is the miracle that we don't live quite long enough to appreciate.