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Mortgage Servicing Assets (Tables)
9 Months Ended
Sep. 30, 2021
Servicing Asset [Abstract]  
Changes in Carrying Amount of Mortgage Servicing Assets
Changes in the carrying amount of commercial mortgage servicing assets are summarized as follows:
 Three months ended September 30,Nine months ended September 30,
Dollars in millions2021202020212020
Balance at beginning of period$600 $565 $578 $539 
Servicing retained from loan sales31 30 88 107 
Purchases8 22 24 
Amortization(30)(29)(89)(88)
Temporary (impairments) recoveries (6)10 (16)
Balance at end of period$609 $566 $609 $566 
Fair value at end of period$735 $685 $735 $685 
Changes in the carrying amount of residential mortgage servicing assets are summarized as follows:
Three months ended September 30,Nine months ended September 30,
Dollars in millions2021202020212020
Balance at beginning of period$77 $46 $58 $46 
Servicing retained from loan sales9 12 32 25 
Purchases —  — 
Amortization(4)(4)(14)(9)
Temporary (impairments) recoveries3 (1)9 (9)
Balance at end of period$85 $53 $85 $53 
Fair value at end of period$89 $54 $89 $54 
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 September 30, 2021, and September 30, 2020, along with the valuation techniques, are shown in the following table: 
dollars in millionsSeptember 30, 2021September 30, 2020
Valuation Technique
Significant
Unobservable Input
Range
Weighted Average
RangeWeighted Average
Discounted cash flowExpected defaults1.00 %2.00 %1.15 %1.00 %2.00 %1.17 %
Residual cash flows discount rate7.64 %10.49 %9.31 %7.72 %10.66 %9.30 %
Escrow earn rate1.04 %1.37 %1.04 %0.92 %1.16 %1.05 %
Loan assumption rate— %1.71 %1.40 %— %1.78 %1.39 %
The range and weighted-average of the significant unobservable inputs used to fair value our mortgage servicing assets at September 30, 2021, and September 30, 2020, along with the valuation techniques, are shown in the following table:
September 30, 2021September 30, 2020
Valuation Technique
Significant
Unobservable Input
RangeWeighted AverageRangeWeighted Average
Discounted cash flowPrepayment speed8.03 %48.88 %11.67 %12.35 %53.36 %16.89 %
Discount rate7.50 %8.57 %7.54 %7.51 %8.80 %7.57 %
Servicing cost$62.00 $4,375 $68.15 $62.00 $5,125 $81.67