The correct answer is option 'C', the President appoints the members of the Finance Commission.

Appointment Authority:
The Finance Commission is appointed by the President of India.

Explanation:
1. Role and Purpose of the Finance Commission:
The Finance Commission is a constitutional body in India that plays a crucial role in the fiscal federalism of the country. Its primary purpose is to recommend the distribution of financial resources between the Union government and the state governments. The Finance Commission is established under Article 280 of the Indian Constitution.

2. Composition of the Finance Commission:
The Finance Commission consists of a Chairman and four other members. These members are appointed by the President of India. Typically, the Chairman is a person with significant experience in public finance or economics, while the other members may include individuals with expertise in various fields such as finance, taxation, or administration.

3. Appointment Process:
The President appoints the members of the Finance Commission based on the recommendations of the Prime Minister. The Prime Minister, in turn, consults various stakeholders such as the Speaker of the Lok Sabha, the Chairman of the Rajya Sabha, the leaders of opposition parties in both houses of Parliament, and other relevant authorities.

4. Tenure and Independence:
The members of the Finance Commission serve a term of five years or until the President reconstitutes the Commission. The Finance Commission operates independently and is not subject to the control or influence of the Union or state governments. This independence ensures that the Commission can make unbiased recommendations regarding the distribution of financial resources.

5. Functions of the Finance Commission:
The Finance Commission performs several functions, including:
- Recommending the principles governing the distribution of tax revenues between the Union government and the state governments.
- Making recommendations on grants-in-aid to states from the Union Consolidated Fund.
- Reviewing the state of finances of both the Union and state governments.
- Suggesting measures to improve the financial position of the states.

In conclusion, the President of India appoints the members of the Finance Commission based on the recommendations of the Prime Minister. The Finance Commission plays a crucial role in the distribution of financial resources between the Union and state governments, and its independence ensures unbiased recommendations.