The Finance Commission in India is a constitutional body that is responsible for recommending the distribution of financial resources between the central government and the state governments. It is appointed by the President of India.

Option 1: The Prime Minister of India does not have the authority to appoint the Finance Commission.

Option 3: The Chairman of the Rajya Sabha also does not have the power to appoint the Finance Commission.

Option 4: Similarly, the Speaker of the Lok Sabha does not have the authority to appoint the Finance Commission.

Therefore, the correct answer is option 2, the President of India. The President appoints the members of the Finance Commission and determines their terms of office.