Fair Value Measurements - Fair Values of Financial Assets and Liabilities, Including Derivative Financial Instruments (Details) - USD ($) $ in Thousands	Sep. 30, 2023	Dec. 31, 2022
Earning assets:
Loans held for sale	$ 0	$ 0
Trading investments	52,561	55,903
Accrued interest receivable, difference	40,833	35,015
Tax indemnification receivable	409,658	380,058
Derivative instruments	0	405
Total earning assets, difference	2,072,183	2,088,881
Interest-bearing liabilities:
Long-term borrowings, difference	381,875	421,881
Derivative instruments	251	0
Total interest-bearing liabilities, difference	669,172	838,340
Excess of net asset fair value over carrying value	2,741,355	2,927,221
Money-market and savings accounts
Interest-bearing liabilities:
Deposits, difference	110,938	104,979
Certificates of deposit
Interest-bearing liabilities:
Deposits, difference	176,359	311,480
Fair Value
Earning assets:
Loans held for sale	0	29,448
Cash and cash equivalents	3,548,225	4,616,117
Trading investments	52,561	55,903
Available-for-sale investments	2,315,978	2,342,089
Accrued interest receivable	1,498,156	1,237,074
Tax indemnification receivable	2,945	2,816
Derivative instruments	17	972
Total earning assets	30,348,413	29,965,153
Interest-bearing liabilities:
Long-term borrowings	5,133,657	4,813,233
Accrued interest payable	99,415	71,586
Derivative instruments	268	567
Total interest-bearing liabilities	26,496,151	25,915,574
Fair Value | Money-market and savings accounts
Interest-bearing liabilities:
Deposits	11,060,884	11,854,849
Fair Value | Certificates of deposit
Interest-bearing liabilities:
Deposits	10,201,927	9,175,339
Carrying Value
Earning assets:
Loans held for sale	0	29,448
Cash and cash equivalents	3,548,225	4,616,117
Trading investments	52,561	55,903
Available-for-sale investments	2,315,978	2,342,089
Accrued interest receivable	1,457,323	1,202,059
Tax indemnification receivable	2,945	2,816
Derivative instruments	17	972
Total earning assets	28,276,230	27,876,272
Interest-bearing liabilities:
Long-term borrowings	5,515,532	5,235,114
Accrued interest payable	99,415	71,586
Derivative instruments	268	567
Total interest-bearing liabilities	27,165,323	26,753,914
Carrying Value | Money-market and savings accounts
Interest-bearing liabilities:
Deposits	11,171,822	11,959,828
Carrying Value | Certificates of deposit
Interest-bearing liabilities:
Deposits	10,378,286	9,486,819
Private Education Loans
Earning assets:
Loans held for investment, net, difference	2,022,371	2,042,835
Private Education Loans | Fair Value
Earning assets:
Loans held for investment, net	22,370,679	21,062,548
Private Education Loans | Carrying Value
Earning assets:
Loans held for investment, net	20,348,308	19,019,713
FFELP Loans
Earning assets:
Loans held for investment, net, difference	8,979	11,031
FFELP Loans | Fair Value
Earning assets:
Loans held for investment, net	559,852	618,186
FFELP Loans | Carrying Value
Earning assets:
Loans held for investment, net	$ 550,873	$ 607,155