The correct option is
A Although he appears to be stingy, he actually spends a lot of money on himself.
The two given sentences contrast each other. We expect that a person who appears stingy does not spend money. The second sentence expresses a contrasting view that he actually spends a lot of money on himself.
Option A: "Although" is a subordinating conjunction of concession which connects two clauses which contrast each other. As the two sentences contrast each other, this is the most appropriate conjunction to be used. This is the correct answer.
Option B: "Not only... but also" is a correlative conjunction which is used to express two clauses which belong to the same parts of speech. If the word which follows "not only" is a verb, then the word which follows "but also" should also be a verb. Here, "not only" is followed by the verb (appears). "But also" is followed by a pronoun (he). A correct usage would be: "He appears not onlystingy but also wicked". Hence, this option is incorrect.
Option C: "So that" is a subordinating conjunction which is used to express cause or reason. It is used to connect two sentences when one is the cause of the other. In the given sentences, the two sentences are not related by cause/ reason, but they contrast each other. Hence, option C is incorrect.
Option D: "As well as" is a replacement for the correlative conjunction "not only... but also". It is a conjunction which is used to connect two clauses which belong to the same part of speech. If the word which precedes "as well as" is a verb, then the word which follows "as well as" should also be a verb. Here, "as well as" is preceded by an adjective (stingy) and followed by a pronoun (he). Hence, this option is incorrect.