You should / could have mentioned that an index persists the column (but only in the index itself) too.
Persisting on the table level safes you a little bit CPU at the costs of disk / memory space when quering the computed column by using the Clustered Index / Key Lookup . When you have a simple calculation (as adding or multiplying two small numbers) and you are not CPU bound, persisting does not always make sense. When you need the computed column only, because a query returns you always the top 50 rows depending on the sum / product, it would be enough to create the computed column non persisted and add an index (who will save the persisted results)
On the other hand, if you use a computed column to save the size or HASH_BYTES() of a VARBINARY(max) column, you should always persists it, since the SQL server otherwise would need to read the whole BLOB columns from disk.