Nicely written as always Ben.
There are two points I'd modify a bit. First, you really aren't "renting out your financial capital." Rather, you're selling your time, at a price that's determined by the difference you can make for one or more employer(s) and/or client(s).
Second, due to the compounding effect, it isn't quite accurate to say you grow rich "slowly, then quickly," which makes it sound as if there's some sort of "step function" in your wealth accumulation, where it's low at first, then jumps up to a higher level.
Rather, it's closer to an exponential function. If R is your annual return on investments (nominal or inflation-adjusted), by contributing an annual amount C to your investments, your wealth after T years should be roughly (((1+R)^(T+1))-1)/R (unless I made a mistake in my math somewhere :)).
I say "closer to" rather than exactly an exponential, because most people don't contribute a constant amount to their investments each year. From my own experience, that amount increased over time, as my income increased faster than my spending (by design).
Bottom line, it seems to be slowly then quickly, because an exponent (especially if the exponent is just a bit higher than 1) starts out pretty flat, and over time gets much higher.
The difference between what you have at the end of the first year and the amount R you contributed at the start of the year is only 10% of R. However, the difference between what you have after 10 years vs. 9 years is 1.6 times R more than the extra R you put in. Then, the difference between year 40 and year 39 is 44.3 times R more than the extra R you put in that year.
So, if your R is say 20% of your income, you only get 2% of your income from portfolio returns in year 1, which grows each year until it's about 32% of your income in year 10, and 4.43 times your income in year 40 (all assuming your income, savings rate, and returns never change).
Sorry for all the nit-picky mathematical details. To simplify, you get rich slowly at first, and then each year a bit faster than the previous year.
In the above example, your investment returns exceed your income around year 26. By year 31 you've accumulated over 200 R, or 20 times your income. That should be enough to allow you to withdraw 4% in year 1 of retirement and cover 80% of your income (which should be enough since you've always invested 20% of your income, which is no longer needed).
