Fair Value Measurements - Fair Values of Financial Assets and Liabilities, Including Derivative Financial Instruments (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
Earning assets:
Loans held for sale	$ 0	$ 0
Trading investments	52,450	37,465
Accrued interest receivable, difference	38,846	100,743
Tax indemnification receivable	305,836	239,578
Derivative instruments	1,121	1,317
Total earning assets, difference	2,001,932	3,409,977
Interest-bearing liabilities:
Long-term borrowings, difference	358,810	(69,184)
Derivative instruments	0	247
Total interest-bearing liabilities, difference	771,724	(151,510)
Excess of net asset fair value over carrying value	2,773,656	3,258,467
Money-market and savings accounts
Interest-bearing liabilities:
Deposits, difference	115,256	(24,799)
Certificates of deposit
Interest-bearing liabilities:
Deposits, difference	297,658	(57,527)
Fair Value
Earning assets:
Loans held for sale	28,880	0
Cash and cash equivalents	4,846,754	4,334,603
Trading investments	52,450	37,465
Available-for-sale investments	2,427,540	2,517,956
Accrued interest receivable	1,262,493	1,306,410
Tax indemnification receivable	8,392	8,047
Derivative instruments	2,172	1,322
Total earning assets	30,214,069	31,856,320
Interest-bearing liabilities:
Long-term borrowings	5,163,501	6,000,174
Accrued interest payable	71,907	46,600
Derivative instruments	1,051	252
Total interest-bearing liabilities	26,099,726	26,956,044
Fair Value | Money-market and savings accounts
Interest-bearing liabilities:
Deposits	11,885,984	11,457,490
Fair Value | Certificates of deposit
Interest-bearing liabilities:
Deposits	8,977,283	9,451,528
Carrying Value
Earning assets:
Loans held for sale	28,880	0
Cash and cash equivalents	4,846,754	4,334,603
Trading investments	52,450	37,465
Available-for-sale investments	2,427,540	2,517,956
Accrued interest receivable	1,223,647	1,205,667
Tax indemnification receivable	8,392	8,047
Derivative instruments	2,172	1,322
Total earning assets	28,212,137	28,446,343
Interest-bearing liabilities:
Long-term borrowings	5,522,311	5,930,990
Accrued interest payable	71,907	46,600
Derivative instruments	1,051	252
Total interest-bearing liabilities	26,871,450	26,804,534
Carrying Value | Money-market and savings accounts
Interest-bearing liabilities:
Deposits	12,001,240	11,432,691
Carrying Value | Certificates of deposit
Interest-bearing liabilities:
Deposits	9,274,941	9,394,001
Private Education Loans
Earning assets:
Loans held for investment, net, difference	1,951,268	3,294,462
Private Education Loans | Fair Value
Earning assets:
Loans held for investment, net	20,932,120	22,919,836
Private Education Loans | Carrying Value
Earning assets:
Loans held for investment, net	18,980,852	19,625,374
FFELP Loans
Earning assets:
Loans held for investment, net, difference	11,818	12,690
FFELP Loans | Fair Value
Earning assets:
Loans held for investment, net	653,268	705,644
FFELP Loans | Carrying Value
Earning assets:
Loans held for investment, net	641,450	692,954
Credit Cards
Earning assets:
Loans held for investment, net, difference	0	2,082
Credit Cards | Fair Value
Earning assets:
Loans held for investment, net	0	25,037
Credit Cards | Carrying Value
Earning assets:
Loans held for investment, net	$ 0	$ 22,955