Each saver is a small world that grows a disk of wealth. The parchment core is every dollar they contributed; the gold rings around it are interest the money earned on its own. Area is money — so when the gold outgrows the parchment, interest has outgrown everything the saver ever put in.
The maths is one line repeated monthly: add this month's contribution, then multiply the whole balance by (1 + rate ÷ 12). Do it for four decades and the multiply, not the adding, does almost all the work — the dashed ring is the exact closed-form total the month-by-month rings climb toward.
This is why an early saver who stops can still outrun a later saver who never does: the early money simply has more years to be multiplied. Dial the return down and the multiply weakens — the head start fades, and whoever put in more money wins instead.
Compounding is time-times-money. At high returns, time dominates and starting early is everything. At low returns, money dominates. The crossover between them is the whole lesson.
This lab hit a snag — the lesson continues without it.