The cost to initiate as a Magic user is 10 + (Grade × 3), so for the first five Grades, the costs are: 13, 16, 19, 22, and 25; totaling 95 Karma. Initiation provides a single benefit from a small list and increases your maximum Magic rating by 1.
The cost to submerge as a Resonance user is 10 × (Grade × 3), so for the first five Grades, the costs are: 30, 60, 90, 120, and 150; totaling 450 Karma. Submersion provides a single benefit from a small list and increases your maximum Resonance rating by 1.
I want this to be a typo so unbelievably badly, but I would not be surprised if it is exactly as intended. However, I have no clue how (or if) this was handled in previous iterations of Shadowrun. The only reason I even ask if others might also think it's just a typo, not the intended usage, is the awkward formula that looks exactly like the Initiation formula.
I believe, if submersion's cost was intended to be calculated as written, it would have been written as (Grade × 30), not the awkward 10 × (Grade × 3) format. It very obviously and deliberately mirrors the format of initiation's 10 + (Grade × 3), making me believe they should be one and the same. The initiation cost appears twice in the book (and is the same, written the same way both times) while the submersion cost appears only the once (and thus has no way to double-check it against a different reference for typos).
Is it a typo, or is as-intended? Obviously, RAW will be very little use here until there's a new errata document or the Matrix book, so any and all explanations are useful, not just RAW citations.