The youngest person to be cryogenically preserved

Some might call them zygotes.

How much does this cost?

In this case, probably $80,000.

This is Alcor, the most established and expensive option. Their list prices are $80,000 for neuro (brain only), $200,000 for whole body preservation [1] There are various funding options. [2]

Cryonics Institute, the other US-based organization, charges $28,000 for full body [3] (they don't offer neuro)

Russian KrioRus charges $12,000 for neuro and $36,000 for full body. [4]

NB: if the cost seems high, keep in mind that most of the money is supposed to be held in trust for the cryonics patient so that income from principal can pay for long-term storage. [5] History proved that it's the only way to reliably and sustainably finance cyopreservation, potentially indefinitely.

I am not affiliated with any cryonics organization, just researching my options.

[1] Alcor FAQ: Cost http://www.alcor.org/FAQs/faq01.html#cost

[2] Alcor: Funding http://www.alcor.org/BecomeMember/sdfunding.htm

[3] Cryonics Institute FAQs: http://www.cryonics.org/about-us/faqs

[4] KrioRus: Human cryopreservation http://kriorus.ru/en/Human-cryopreservation

[5] Cryonics FAQ by by Ben Best http://www.benbest.com/cryonics/CryoFAQ.html#_IIIG_

Serious question: what's to salvage from the brain of a terminal brain cancer child? This strikes me as a very silly way to preserve a human being. If they really wanted to give their child a "chance" to live a full life, they should have cryogenized her sooner, no? (It might be illegal, though.)

The serious answer is that resuscitation of cryopreserved humans is not currently possible and has never been done. We have no idea whether anything from the brain or the body is salvageable, nor whether starting sooner or later makes any difference.

Perhaps one way to think about it is that cryopreservation is a modern alternative to a grave burial, and the thing most salvaged is the hope and memories in the family and friends of the deceased.