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explain and show mathmatically how to get the expected value by 2025

Apple's Services business has emerged as the company's second-largest segment, following the iPhone, posting revenues of $46 billion in FY'19. The business has grown at a CAGR of 21% over the last 5 years, compared to just about 7% for the iPhone, and gross margins are also significantly thicker compared to the hardware business (63% versus 32% in FY'19). It's also likely that the increasing mix of services revenue has contributed to the rally in Apple's stock, which is up 50%+ over the last six months. In this analysis, we try to break down the various drivers of the services business, using select figures that Apple discloses and other publicly available data. We also outline how the Services segment could generate more gross profits than the iPhone by the year 2025 if revenues grow at mid-to-high teens levels, while the iPhone continues to post low single-digit levels of growth. Apple's Services business has emerged as the company's second-largest segment, following the iPhone, posting revenues of $46 billion in FY'19. The business has grown at a CAGR of 21% over the last 5 years, compared to just about 7% for the iPhone, and gross margins are also significantly thicker compared to the hardware business (63% versus 32% in FY'19). It's also likely that the increasing mix of services revenue has contributed to the rally in Apple's stock, which is up 50%+ over the last six months. In this analysis, we try to break down the various drivers of the services business, using select figures that Apple discloses and other publicly available data. We also outline how the Services segment could generate more gross profits than the iPhone by the year 2025 if revenues grow at mid-to-high teens levels, while the iPhone continues to post low single-digit levels of growth

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