NEW YORK, April 5 (Reuters) - Credit Suisse will announce the departure of two senior executives and detail how much it expects to lose through its exposure to family office Archegos in an investor update Tuesday, sources familiar with the matter said. The Swiss bank will say that Chief Risk Officer Lara Warner and Brian Chin, CEO of its investment bank, will leave the bank, the sources said on Monday. (Reporting by Matt Scuffham; Editing by Leslie Adler)