Compounding and its magic!

Let's start with the famous "rice and the chessboard story". Once upon a time, there lived a king who was a chess enthusiast. He beat every known player. To motivate his opponents, the king would give any reward that they ask for, provided they were successful in beating the king. One day, he was challenged by a travelling sage to a game of chess. The king obliged and asked the sage to name a prize for himself if he wins.