Whenever the claim or defense asserted in the amended pleading arose out of the conduct, transaction, or occurrence set forth or attempted to be set forth in the original pleading, the amendment relates back to the date of the original pleading. An amendment changing the party against whom a claim is asserted relates back if the foregoing provision is satisfied and, within the period provided by law for commencing the action against him, the party to be brought in by amendment:
SDCL 15-6-15(c)