It seems churlish to keep pointing this out, but (assuming the investment is consistent with the typical Silicon Valley practice), it is just not true that this investment, or any participant, has now valued the company at $3.5 billion.
Stripe has sold the investors a new round of senior preferred shares (again, making assumptions). These shares carry various bells and whistles whose terms we don't know -- but probably include some preference at an unknown rate.
The seniority and the bells and whistles make these shares particularly valuable, compared with less-senior preferred shares, not to mention common shares, not to mention something like an authorized stock option that will be issued in-the-money at some future time.
The way you would get $3.5 billion (again, making the same assumptions) is by imputing this per-share value to all of the equity units, as well as things like authorized-but-not-yet-issued stock options.
That is not sensible. The investors in this round have not acted in a way that suggests they believe the less-privileged shares are worth as much as these new shares, and neither has anybody else. There is no basis for imputing the same value to all equity units (and authorized options, irrespective of strike price).
Here is a hypothetical cap table that is consistent with public reports: http://qr.ae/lc0ry
Previously on HN: https://news.ycombinator.com/item?id=5798905