What's the difference in Lump Sum vs. Automated Investments?

I know you have posted about the differences in how much someone can make by trying to time the market vs. automatic transfers to their investment accounts. Loved the example of how much each person made after 41 years. However, I was curious if you had a theoretical example of a person investing a lump sum (you can pick the amount) versus automating for x amount of years for the same amount invested in the long run.

BONUS: How would it change if you had the same amount invested but dispersed among 3 different accounts (ie. IRA, 401k, and brokerage)? Mathematically it would make less because the exponential increase of the investment in one account would increase at a greater rate than if it were dispersed in three different accounts. Just want to make sure I’m correct in this.

Check out this article:

And the associated calculator:

Regarding your bonus, splitting between three accounts absolutely does not hurt the exponential growth. i.e. three accounts of $10K each will grow (in total) at the exact same rate as one account of $30K. So yeah, you’d want to prioritize the tax advantaged accounts when you can!