Please reason step by step, and put your final answer within \boxed{}.
Mr. Grey's house was worth $100,000. He sold the house to Mr. Brown at a profit of 10%. After one year, Mr. Brown decided to invest some money in renovations and spent 5% of the purchasing price on improvements. Then, Mr. Brown sold the house to his friend Mr. Green with a 7% profit. Mr. Green rented out the house for two years, earning a total rent income of 20% of his purchasing cost. After two years, Mr. Green sold the house back to Mr. Brown with a 10% loss. How much was Mr. Brown's final purchase price after buying the house back from Mr. Green?
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