Allowance for Loan Losses - Allowance and Recorded Investments in Loans (Detail) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2018 USD ($) charge_off	Sep. 30, 2017 USD ($) charge_off	Sep. 30, 2018 USD ($) charge_off	Sep. 30, 2017 USD ($) charge_off
Allowance for Loan Losses
Allowance at beginning of period	$ 295,277	$ 207,448	$ 251,475	$ 184,701
Total provision	68,896	53,847	187,339	130,524
Net charge-offs:
Charge-offs	(40,221)	(34,681)	(124,458)	(94,133)
Recoveries	5,022	4,562	15,834	12,218
Net charge-offs	(35,199)	(30,119)	(108,624)	(81,915)
Loan sales	0	(1,257)	(1,216)	(3,391)
Allowance at end of period	328,974	229,919	328,974	229,919
Allowance:
Ending balance: individually evaluated for impairment	119,643	100,999	119,643	100,999
Ending balance: collectively evaluated for impairment	209,331	128,920	209,331	128,920
Loans:
Ending balance: individually evaluated for impairment	1,199,493	942,561	1,199,493	942,561
Ending balance: collectively evaluated for impairment	21,040,289	17,271,626	21,040,289	17,271,626
FFELP Loans
Allowance for Loan Losses
Allowance at beginning of period	1,073	1,606	1,132	2,171
Total provision	259	(73)	742	(161)
Net charge-offs:
Charge-offs	(252)	(181)	(794)	(658)
Recoveries	0	0	0	0
Net charge-offs	(252)	(181)	(794)	(658)
Loan sales	0	0	0	0
Allowance at end of period	1,080	1,352	1,080	1,352
Allowance:
Ending balance: individually evaluated for impairment	0	0	0	0
Ending balance: collectively evaluated for impairment	1,080	1,352	1,080	1,352
Loans:
Ending balance: individually evaluated for impairment	0	0	0	0
Ending balance: collectively evaluated for impairment	$ 866,786	$ 949,180	$ 866,786	$ 949,180
Net charge-offs as a percentage of average loans in repayment (annualized)	0.15%	0.10%	0.15%	0.12%
Allowance as a percentage of the ending total loan balance	0.12%	0.14%	0.12%	0.14%
Allowance as a percentage of the ending loans in repayment	0.16%	0.20%	0.16%	0.20%
Allowance coverage of net charge-offs (annualized) | charge_off	1.07	1.87	1.02	1.54
Ending total loans, gross	$ 866,786	$ 949,180	$ 866,786	$ 949,180
Average loans in repayment	681,131	734,613	700,679	752,990
Ending loans in repayment	679,110	690,849	679,110	690,849
Private Education Loans
Allowance for Loan Losses
Allowance at beginning of period	261,695	205,024	243,715	182,472
Total provision	42,482	53,120	130,616	129,105
Net charge-offs:
Charge-offs	(34,229)	(34,280)	(113,852)	(93,235)
Recoveries	4,736	4,560	15,421	12,216
Net charge-offs	(29,493)	(29,720)	(98,431)	(81,019)
Loan sales	0	(1,257)	(1,216)	(3,391)
Allowance at end of period	274,684	227,167	274,684	227,167
Allowance:
Ending balance: individually evaluated for impairment	119,643	100,999	119,643	100,999
Ending balance: collectively evaluated for impairment	155,041	126,168	155,041	126,168
Loans:
Ending balance: individually evaluated for impairment	1,199,493	942,561	1,199,493	942,561
Ending balance: collectively evaluated for impairment	$ 19,040,498	$ 16,190,346	$ 19,040,498	$ 16,190,346
Net charge-offs as a percentage of average loans in repayment (annualized)	0.88%	1.08%	1.01%	1.02%
Allowance as a percentage of the ending total loan balance	1.36%	1.33%	1.36%	1.33%
Allowance as a percentage of the ending loans in repayment	1.99%	1.99%	1.99%	1.99%
Allowance coverage of net charge-offs (annualized) | charge_off	2.33	1.91	2.09	2.10
Ending total loans, gross	$ 20,239,991	$ 17,132,907	$ 20,239,991	$ 17,132,907
Average loans in repayment	13,351,517	10,971,028	13,009,704	10,589,725
Ending loans in repayment	13,815,415	11,406,581	13,815,415	11,406,581
Personal Loans
Allowance for Loan Losses
Allowance at beginning of period	32,509	818	6,628	58
Total provision	26,155	800	55,981	1,580
Net charge-offs:
Charge-offs	(5,740)	(220)	(9,812)	(240)
Recoveries	286	2	413	2
Net charge-offs	(5,454)	(218)	(9,399)	(238)
Loan sales	0	0	0	0
Allowance at end of period	53,210	1,400	53,210	1,400
Allowance:
Ending balance: individually evaluated for impairment	0	0	0	0
Ending balance: collectively evaluated for impairment	53,210	1,400	53,210	1,400
Loans:
Ending balance: individually evaluated for impairment	0	0	0	0
Ending balance: collectively evaluated for impairment	$ 1,133,005	$ 132,100	$ 1,133,005	$ 132,100
Net charge-offs as a percentage of average loans in repayment (annualized)	2.03%	0.96%	1.56%	0.51%
Allowance as a percentage of the ending total loan balance	4.70%	1.06%	4.70%	1.06%
Allowance as a percentage of the ending loans in repayment	4.70%	1.06%	4.70%	1.06%
Allowance coverage of net charge-offs (annualized) | charge_off	2.44	1.60	4.25	4.41
Ending total loans, gross	$ 1,133,005	$ 132,100	$ 1,133,005	$ 132,100
Average loans in repayment	1,072,624	90,850	803,928	62,747
Ending loans in repayment	$ 1,133,005	$ 132,100	$ 1,133,005	$ 132,100