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Segment Analysis - Segment Reporting (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
Jun. 30, 2024
Jun. 30, 2023
Jun. 30, 2024
Jun. 30, 2023
Sep. 30, 2023
Segment Reporting Information [Line Items]          
Total revenues $ 27,069.7 $ 15,047.9 $ 68,748.8 $ 44,220.5  
Operating revenues: 913.7 776.9 2,516.1 2,136.1  
Net operating revenues (loss): 468.5 435.9 1,312.4 1,217.3  
Net contribution: 377.3 340.8 1,043.1 949.1  
Segment income 243.7 207.9 664.5 560.2  
Net operating revenue (loss) with Corporate (26.9) (14.1) (55.3) (47.0)  
Overhead costs and expenses (128.8) (99.3) (353.2) (289.1)  
Gain on acquisition 0.0 0.0 0.0 23.5  
Income before tax 88.0 94.5 256.0 247.6  
Assets 25,930.8   25,930.8   $ 21,938.7
Corporate          
Segment Reporting Information [Line Items]          
Total revenues 8.3 8.6 31.9 23.9  
Operating revenues: 8.3 8.6 31.9 23.9  
Net operating revenues (loss): (26.9) (14.1) (55.3) (47.0)  
Assets 932.2   932.2   812.3
Eliminations          
Segment Reporting Information [Line Items]          
Total revenues (13.0) (10.2) (36.6) (29.1)  
Operating revenues: (13.0) (10.2) (36.6) (29.1)  
Commercial          
Segment Reporting Information [Line Items]          
Net contribution: 168.7 156.9 414.4 413.5  
Segment income 125.7 117.0 298.5 302.7  
Commercial | Operating Segments          
Segment Reporting Information [Line Items]          
Total revenues 26,410.3 14,444.5 66,867.4 42,188.7  
Operating revenues: 262.2 252.7 661.1 655.2  
Net operating revenues (loss): 220.5 213.6 548.1 551.4  
Assets 4,743.7   4,743.7   4,676.3
Institutional          
Segment Reporting Information [Line Items]          
Net contribution: 104.8 81.7 307.5 265.6  
Segment income 62.2 45.1 188.7 162.9  
Institutional | Operating Segments          
Segment Reporting Information [Line Items]          
Total revenues 508.9 381.1 1,408.0 1,087.1  
Operating revenues: 508.9 381.1 1,408.0 1,087.1  
Net operating revenues (loss): 157.7 120.3 456.1 401.4  
Assets 18,635.7   18,635.7   15,059.3
Retail          
Segment Reporting Information [Line Items]          
Net contribution: 63.7 60.3 196.2 147.9  
Segment income 27.6 17.2 89.5 17.8  
Retail | Operating Segments          
Segment Reporting Information [Line Items]          
Total revenues 104.1 170.7 317.1 791.5  
Operating revenues: 96.2 91.5 290.7 240.6  
Net operating revenues (loss): 68.5 65.1 209.8 159.8  
Assets 1,056.9   1,056.9   1,014.2
Payments          
Segment Reporting Information [Line Items]          
Net contribution: 40.1 41.9 125.0 122.1  
Segment income 28.2 28.6 87.8 76.8  
Payments | Operating Segments          
Segment Reporting Information [Line Items]          
Total revenues 51.1 53.2 161.0 158.4  
Operating revenues: 51.1 53.2 161.0 158.4  
Net operating revenues (loss): 48.7 $ 51.0 153.7 $ 151.7  
Assets $ 562.3   $ 562.3   $ 376.6