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Mortgage Servicing Assets (Tables)
6 Months Ended
Jun. 30, 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 June 30,
 
Six months ended June 30,
in millions
2019

2018

 
2019

2018

Balance at beginning of period
$
38

$
32

 
$
37

$
31

Servicing retained from loan sales
2

3

 
4

5

Purchases


 


Amortization
(1
)
(1
)
 
(2
)
(2
)
Balance at end of period
$
39

$
34

 
$
39

$
34

Fair value at end of period
$
45

$
43

 
$
45

$
43

 
 
 
 
 
 

Changes in the carrying amount of commercial mortgage servicing assets are summarized as follows:
 
Three months ended June 30,
 
Six months ended June 30,
in millions
2019

2018

 
2019

2018

Balance at beginning of period
$
497

$
435

 
$
502

$
412

Servicing retained from loan sales
23

29

 
41

56

Purchases
17

12

 
23

33

Amortization
(28
)
(25
)
 
(57
)
(50
)
Balance at end of period
$
509

$
451

 
$
509

$
451

Fair value at end of period
$
723

$
646

 
$
723

$
646

 
 
 
 
 
 

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 June 30, 2019, and June 30, 2018, along with the valuation techniques, are shown in the following table: 
 
dollars in millions
 
June 30, 2019
 
June 30, 2018
 
Valuation Technique
Significant
Unobservable Input
Range
(Weighted Average)
 
 
Discounted cash flow
Expected defaults
1.00 - 2.00% (1.13%)
 
1.00 - 3.00% (1.17%)
 
 
Residual cash flows discount rate
7.00 - 11.54% (9.26%)
 
7.00 - 15.00% (9.06%)
 
 
Escrow earn rate
1.92 - 3.13% (2.63%)
 
2.40 - 3.82% (3.10%)
 
 
Loan assumption rate
0.00 - 3.02% (1.40%)
 
0.00 - 3.00% (1.19%)

The range and weighted-average of the significant unobservable inputs used to fair value our mortgage servicing assets at June 30, 2019, and June 30, 2018, along with the valuation techniques, are shown in the following table:
 
dollars in millions
 
June 30, 2019
 
June 30, 2018
 
Valuation Technique
Significant
Unobservable Input
Range
(Weighted Average)
 
 
Discounted cash flow
Prepayment speed
10.95 - 62.06% (12.52%)
 
8.39 - 49.39% (9.17%)
 
 
Discount rate
7.50 - 10.00% (7.53%)
 
8.50 - 11.00% (8.54%)
 
 
Servicing cost
$62 - $4,375 ($67.55)
 
$76 - $4,385 ($82.38)