Hash Time-Lock Contracts (HTLCs)

Hash Time-Lock Contracts (HTLCs) seem to be the method by which the correct amount gets sent to the final recipient, the correct fees are taken at each hop/node, and that it is done within a certain time.  My understanding now is the following.  Assume node A wants to send to node D 10,000 Sats.  They don't have a direct connection, so it will go through nodes B and C.  If B's node will charge 5 Sats and C's node will charge 4 Sats, then A sends 10,009 Sats in an HTLC so that exactly 10,000 Sats will arrive to D after all the steps are completed.