The bank has $14 billion of reserves to cover rep and warranty claims for bad mortgages.
Moynihan was speaking at the Goldman Sachs Financial Services Conference in Manhattan Tuesday.
BofA has already paid $43 billion in litigation and repurchase costs related to mortgages, according to Moynihan's presentation.
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But that has settled a lot of key mortgage issues for BofA. One of the biggest is the bank's exposure to claims from Fannie Mae and Freddie Mac for mortgages they bought from various units of BofA.
In addition, BofA has settled claims from mortgage insurers MBIA, Assured Guaranty and Syncora, which insured mortgages that went bad. BofA's costs also include claims from investors in mortgage-backed securities created with bad loans from Countrywide Financial, which BofA bought in 2008.
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Beyond what it has already paid, and has reserved for, BofA still expects to pay up to $5.1 billion in mortgage-related litigation costs.
Future additional costs for mortgage representations and warranties could run up to $4 billion according to Moynihan's presentation.
-By CNBC's Margaret Popper. Follow her on Twitter @popperm.
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