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Fair Value Measurements - Fair Values of Financial Assets and Liabilities, Including Derivative Financial Instruments (Details) - USD ($)
$ in Thousands
Sep. 30, 2020
Dec. 31, 2019
Earning assets    
Trading investments $ 14,651 $ 0
Accrued interest receivable, difference 94,501 98,746
Tax indemnification receivable 505,208 88,844
Total earning assets, difference 3,481,411 2,265,887
Interest-bearing liabilities    
Long-term borrowings, difference (189,085) (80,286)
Total interest-bearing liabilities, difference (489,482) (226,078)
Excess of net asset fair value over carrying value 2,991,929 2,039,809
Money-market and savings accounts    
Interest-bearing liabilities    
Deposits, difference (74,432) (28,528)
Certificates of deposit    
Interest-bearing liabilities    
Deposits, difference (225,965) (117,264)
Fair Value    
Earning assets    
Cash and cash equivalents 4,351,045 5,563,877
Trading investments 14,651 0
Available-for-sale investments 2,090,707 487,669
Accrued interest receivable 1,567,103 1,491,471
Tax indemnification receivable 28,256 27,558
Derivative instruments 541 715
Total earning assets 33,148,984 34,406,223
Interest-bearing liabilities    
Short-term borrowings 0 289,230
Long-term borrowings 5,136,732 4,434,323
Accrued interest payable 75,196 75,158
Derivative instruments 0 1,164
Total interest-bearing liabilities 28,621,763 29,228,573
Fair Value | Money-market and savings accounts    
Interest-bearing liabilities    
Deposits 10,944,983 10,363,691
Fair Value | Certificates of deposit    
Interest-bearing liabilities    
Deposits 12,464,852 14,065,007
Carrying Value    
Earning assets    
Cash and cash equivalents 4,351,045 5,563,877
Trading investments 14,651 0
Available-for-sale investments 2,090,707 487,669
Accrued interest receivable 1,472,602 1,392,725
Tax indemnification receivable 28,256 27,558
Derivative instruments 541 715
Total earning assets 29,667,573 32,140,336
Interest-bearing liabilities    
Short-term borrowings 0 289,230
Long-term borrowings 4,947,647 4,354,037
Accrued interest payable 75,196 75,158
Derivative instruments 0 1,164
Total interest-bearing liabilities 28,132,281 29,002,495
Carrying Value | Money-market and savings accounts    
Interest-bearing liabilities    
Deposits 10,870,551 10,335,163
Carrying Value | Certificates of deposit    
Interest-bearing liabilities    
Deposits 12,238,887 13,947,743
Private Education Loans    
Earning assets    
Loans held for investment, net, difference 3,373,050 2,092,426
Private Education Loans | Fair Value    
Earning assets    
Loans held for investment, net 24,328,972 24,988,941
Private Education Loans | Carrying Value    
Earning assets    
Loans held for investment, net 20,955,922 22,896,515
FFELP Loans    
Earning assets    
Loans held for investment, net, difference 13,519 11,239
FFELP Loans | Fair Value    
Earning assets    
Loans held for investment, net 756,739 795,055
FFELP Loans | Carrying Value    
Earning assets    
Loans held for investment, net 743,220 783,816
Personal Loans    
Earning assets    
Loans held for investment, net, difference 0 63,476
Personal Loans | Fair Value    
Earning assets    
Loans held for investment, net 0 1,047,119
Personal Loans | Carrying Value    
Earning assets    
Loans held for investment, net 0 983,643
Credit Cards    
Earning assets    
Loans held for investment, net, difference 341 0
Credit Cards | Fair Value    
Earning assets    
Loans held for investment, net 10,970 3,818
Credit Cards | Carrying Value    
Earning assets    
Loans held for investment, net $ 10,629 $ 3,818