At September 30, 2019, loan servicing rights derived from loans sold with servicing retained totaled $24.6 million, compared to $24.5 million at December 31, 2018. Loans serviced for others are not reported as assets. The principal balance of loans serviced for others was $3.379 billion at September 30, 2019, compared to $3.306 billion at December 31, 2018. Approximately 99.7% of the loans serviced for others at September 30, 2019 were residential mortgage loans. Custodial escrow balances maintained in connection with serviced loans were $43.6 million at September 30, 2019 and $10.7 million at December 31, 2018.

The following table summarizes the carrying values and activity related to loan servicing rights and the related valuation allowance for the three and nine months ended September 30, 2019 and 2018:

	Three Months Ended						Nine Months Ended
	September 30,						September 30,
(dollars in thousands)	2019			2018			2019			2018
Balance at beginning of period	$	24,364		$	24,318		$	24,512		$	24,690
Additions		2,097			1,147			4,026			3,098
Amortization		(1,717	)		(1,117	)		(3,794	)		(3,440	)
Balance before valuation allowance at end of period		24,744			24,348			24,744			24,348
Valuation allowance:
Balance at beginning of period		(32	)		(15	)		(15	)		(29	)
(Additions)/recoveries		(89	)		3			(106	)		17
Balance at end of period		(121	)		(12	)		(121	)		(12	)
Loan servicing rights, net	$	24,623		$	24,336		$	24,623		$	24,336

At September 30, 2019, the fair value of servicing rights was $25.5 million, which was determined using a discount rate of 12% and a weighted average prepayment speed of 170% PSA. At December 31, 2018, the fair value of servicing rights was $27.4 million, which was determined using a discount rate of 12% and a weighted average prepayment speed of 119% PSA.