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Allowance for Loan Losses - Loan Status and Aging of Past Due TDR Loans (Detail) - USD ($)
$ in Thousands
Sep. 30, 2018
Jun. 30, 2018
Dec. 31, 2017
Sep. 30, 2017
Jun. 30, 2017
Dec. 31, 2016
TDR loans in repayment and percentage of each status:            
Allowance for loan losses $ (328,974) $ (295,277) $ (251,475) $ (229,919) $ (207,448) $ (184,701)
Loans held for investment, net 21,978,903   18,567,641      
Student Loan | Consumer Portfolio Segment | Troubled Debt Restructured Loans            
Accounts, Notes, Loans and Financing Receivable [Line Items]            
TDR loans in in-school/grace/deferment 68,848   51,745      
TDR loans in forbearance 73,403   69,652      
TDR loans in repayment and percentage of each status:            
Loans current 954,309   774,222      
Total TDR loans in repayment $ 1,057,242   $ 868,954      
Loans current (as a percentage) 90.30%   89.10%      
Total TDR loans in repayment 100.00%   100.00%      
Total Private Education Loans, gross $ 1,199,493   $ 990,351      
Student Loan | Consumer Portfolio Segment | Loans delinquent 31-60 days | Troubled Debt Restructured Loans            
TDR loans in repayment and percentage of each status:            
Loans delinquent $ 51,979   $ 48,377      
Loans delinquent (as a percentage) 4.90%   5.60%      
Student Loan | Consumer Portfolio Segment | Loans delinquent 61-90 days | Troubled Debt Restructured Loans            
TDR loans in repayment and percentage of each status:            
Loans delinquent $ 31,582   $ 28,778      
Loans delinquent (as a percentage) 3.00%   3.30%      
Student Loan | Consumer Portfolio Segment | Loans delinquent, greater than 90 days | Troubled Debt Restructured Loans            
TDR loans in repayment and percentage of each status:            
Loans delinquent $ 19,372   $ 17,577      
Loans delinquent (as a percentage) 1.80%   2.00%