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Mortgage Servicing Assets (Tables)
3 Months Ended
Mar. 31, 2019
Servicing Asset [Abstract]  
Changes in Carrying Amount of Mortgage Servicing Assets Changes in the carrying amount of residential mortgage servicing assets are summarized as follows:
 
Three months ended March 31,
in millions
2019

2018

Balance at beginning of period
$
37

$
31

Servicing retained from loan sales
2

2

Purchases


Amortization
(1
)
(1
)
Balance at end of period
$
38

$
32

Fair value at end of period
$
50

$
42

 
 
 
Changes in the carrying amount of commercial mortgage servicing assets are summarized as follows:
 
Three months ended March 31,
in millions
2019

2018

Balance at beginning of period
$
502

$
412

Servicing retained from loan sales
18

27

Purchases
6

21

Amortization
(29
)
(25
)
Balance at end of period
$
497

$
435

Fair value at end of period
$
727

$
537

 
 
 
Schedule of Range and Weighted-Average of Significant Unobservable Inputs The range and weighted average of the significant unobservable inputs used to determine the fair value of our commercial mortgage servicing assets at March 31, 2019, and March 31, 2018, along with the valuation techniques, are shown in the following table: 
 
dollars in millions
 
March 31, 2019
 
March 31, 2018
 
Valuation Technique
Significant
Unobservable Input
Range
(Weighted Average)
 
 
Discounted cash flow
Expected defaults
1.00 - 2.00% (1.14%)
 
1.00 - 3.00% (1.18%)
 
 
Residual cash flows discount rate
7.00 - 15.00% (9.19%)
 
7.00 - 15.00% (8.99%)
 
 
Escrow earn rate
2.22 - 3.70% (2.98%)
 
2.17 - 3.45% (2.84%)
 
 
Loan assumption rate
0.00 - 3.18% (1.39%)
 
0.00 - 2.84% (1.18%)

The range and weighted-average of the significant unobservable inputs used to fair value our mortgage servicing assets at March 31, 2019, and March 31, 2018, along with the valuation techniques, are shown in the following table:
 
dollars in millions
 
March 31, 2019
 
March 31, 2018
 
Valuation Technique
Significant
Unobservable Input
Range
(Weighted Average)
 
 
Discounted cash flow
Prepayment speed
9.32 - 58.76% (9.93%)
 
8.37 - 48.63% (9.12%)
 
 
Discount rate
7.50 - 10.00% (7.54%)
 
8.50 - 11.00% (8.54%)
 
 
Servicing cost
$62 - $4,375 ($68.23)
 
$76 - $4,385 ($83.05)