flows at risk-adjusted rates.
The model considers portfolio characteristics, contractually specified servicing fees, prepayment assumptions, delinquency rates, late charges, other ancillary revenue and costs to service, and other economic factors.
The Firm reassesses and periodically adjusts the underlying inputs and assumptions used in the OAS model to reflect market conditions and assumptions that a market participant would consider in valuing the MSR asset.
During the fourth quarter of the 2007, the Firm’s proprietary prepayment model was refined to reflect a decrease in estimated future mortgage prepayments based upon a number of market related factors including a downward trend in home prices, general tightening of credit underwriting standards and the associated impact on refinancing activity.
The Firm compares fair value estimates and assumptions to observable market data where available and to recent market activity and actual portfolio experience.
The fair value of MSRs is sensitive to changes in interest rates, including their effect on prepayment speeds.
JPMorgan Chase uses or has used combinations of derivatives, AFS securities and trading instruments to manage changes in the fair value of MSRs.
The intent is to offset any changes in the fair value of MSRs with changes in the fair value of the related risk management instruments.
MSRs decrease in value when interest rates decline.
Conversely, securities (such as mortgage-backed securities), principal-only certificates and certain derivatives (when the Firm receives fixed-rate interest payments) increase in value when interest rates decline.
In March 2006, the FASB issued SFAS 156, which permits an entity a one-time irrevocable election to adopt fair value accounting for a class of servicing assets.
JPMorgan Chase elected to adopt the standard effective January 1, 2006, and defined MSRs as one class of servicing assets for this election.
At the transition date, the fair value of the MSRs exceeded their carrying amount, net of any related valuation allowance, by $150 million net of taxes.
This amount was recorded as a cumulative-effect adjustment to retained earnings as of January 1, 2006.
MSRs are recognized in the Consolidated balance sheet at fair value, and changes in their fair value are recorded in currentperiod earnings.
Revenue amounts related to MSRs and the financial instruments used to manage the risk of MSRs are recorded in Mortgage fees and related income.
For the year ended December 31, 2005, MSRs were accounted for under SFAS 140, using a lower of cost or fair value approach.
Under this approach, MSRs were amortized as a reduction of the actual servicing income received in proportion to, and over the period of, the estimated future net servicing income stream of the underlying mortgage loans.
For purposes of evaluating and measuring impairment of MSRs, the Firm stratified the portfolio on the basis of the predominant risk characteristics, which are loan type and interest rate.
Any indicated impairment was recognized as a reduction in revenue through a valuation allowance, which represented the extent to which the carrying value of an individual stratum exceeded its estimated fair value.
Any gross carrying value and relat ed valuation allowance amounts which were not expected to be recovered in the foreseeable future, based upon the interest rate scenario, were considered to be other-than-temporary.
Prior to the adoption of SFAS 156, the Firm designated certain derivatives used to risk manage MSRs (e. g. , a combination of swaps, swaptions and floors) as SFAS 133 fair value hedges of benchmark interest rate risk.
SFAS 133 hedge accounting allowed the carrying value of the hedged MSRs to be adjusted through earnings in the same period that the change in value of the hedging derivatives was recognized through earnings.
The designated hedge period was daily.
In designating the benchmark interest rate, the Firm considered the impact that the change in the benchmark rate had on the prepayment speed estimates in determining the fair value of the MSRs.
Hedge effectiveness was assessed using a regression analysis of the change in fair value of the MSRs as a result of changes in benchmark interest rates and of the change in the fair value of the designated derivatives.
The valuation adjustments to both the MSRs and SFAS 133 derivatives were recorded in Mortgage fees and related income.
With the election to apply fair value accounting to the MSRs under SFAS 156, SFAS 133 hedge accounting is no longer necessary.
For a further discussion on derivative instruments and hedging activities, see Note 30 on pages 168–169 of this Annual Report.
The following table summarizes MSR activity, certain key assumptions, and the sensitivity of the fair value of MSRs to adverse changes in those key assumptions for the years ended December 31, 2007 and 2006, during which period MSRs were accounted for under SFAS 156.
## Table 0 ##
(a) Represents MSR asset fair value adjustments due to changes in market-based inputs, such as interest rates and volatility, as well as updates to assumptions used in the MSR valuation model.
This caption also represents total realized and unrealized gains (losses) included in Net income per the SFAS 157 disclosure for fair value measurement using significant unobservable inputs (level 3).
These changes in fair value are recorded in Mortgage fees and related income.
(b) Includes changes in the MSR value due to modeled servicing portfolio runoff (or time decay).
This caption represents the impact of cash settlements per the SFAS 157 disclosure for fair value measurement using significant unobservable inputs (level 3).
These changes in fair value are recorded in Mortgage fees and related income.
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS JPMorgan Chase & Co.  164 JPMorgan Chase & Co.  / 2007 Annual Report Note 26 – Income taxes In June 2006, the FASB issued FIN 48, which clarifies the accounting for uncertainty in income taxes recognized under SFAS 109.
FIN 48 addresses the recognition and measurement of tax positions taken or expected to be taken, and also provides guidance on derecognition, classification, interest and penalties, accounting in interim periods and disclosure.
The Firm adopted and applied FIN 48 under the transition provisions to all of its income tax positions at the required effective date of January 1, 2007, resulting in a $436 million cumulative effect increase to Retained earnings, a reduction in Goodwill of $113 million and a $549 million decrease in the liability for income taxes.
JPMorgan Chase and eligible subsidiaries file a consolidated U. S.  federal income tax return.
JPMorgan Chase uses the asset-and-liability method required by SFAS 109 to provide income taxes on all transactions recorded in the Consolidated financial statements.
This method requires that income taxes reflect the expected future tax consequences of temporary differences between the carrying amounts of assets or liabilities for book and tax purposes.
Accordingly, a deferred tax liability or asset for each temporary difference is determined based upon the tax rates that the Firm expects to be in effect when the underlying items of income and expense are realized.
JPMorgan Chase’s expense for income taxes includes the current and deferred portions of that expense.
A valuation allowance is established to reduce deferred tax assets to the amount the Firm expects to realize.
Due to the inherent complexities arising from the nature of the Firm’s businesses, and from conducting business and being taxed in a substantial number of jurisdictions, significant judgments and estimates are required to be made.
Agreement of tax liabilities between JPMorgan Chase and the many tax jurisdictions in which the Firm files tax returns may not be finalized for several years.
Thus, the Firm’s final tax-related assets and liabilities may ultimately be different than those currently reported.
At December 31, 2007, and January 1, 2007, JPMorgan Chase’s unrecognized tax benefits, excluding related interest expense and penalties, was $4.8 billion and $4.7 billion, respectively, of which $1.3 billion and $1.0 billion, if recognized, would reduce the annual effective tax rate.
As JPMorgan Chase is presently under audit by a number of tax authorities, it is reasonably possible that unrecognized tax benefits could change significantly over the next 12 months.
JPMorgan Chase does not expect that any such changes would have a material impact on its annual effective tax rate.
The following table presents a reconciliation of the beginning and ending amount of unrecognized tax benefits for the year ended December 31, 2007.
## Table 1 ##
Pretax interest expense and penalties related to income tax liabilities recognized in Income tax expense was $516 million ($314 million after-tax) in 2007.
Included in Accounts payable, accrued expense and other liabilities at January 1, 2007, in addition to the Firm’s liability for unrecognized tax benefits, was $1.3 billion for income tax-related interest and penalties, of which the penalty component was insignificant.
Accrued income tax-related interest and penalties increased to $1.6 billion at December 31, 2007, due to the continuing outstanding status of the unrecognized tax benefit liability, the penalty component of which remains insignificant.
JPMorgan Chase is subject to ongoing tax examinations by the tax authorities of the various jurisdictions in which it operates, including U. S.  federal, state and non-U.
S.  jurisdictions.
The Firm’s consolidated federal income tax returns are presently under examination by the Internal Revenue Service (IRS) for the years 2003, 2004 and 2005.
The consolidated federal income tax returns of heritage Bank One Corporation, which merged with and into JPMorgan Chase on July 1, 2004, are under examination for the years 2000 through 2003, and for the period January 1, 2004, through July 1, 2004.
Both examinations are expected to conclude in the latter part of 2008.
The IRS audit of the 2006 consolidated federal income tax return has not yet commenced.
Certain administrative appeals are pending with the IRS relating to prior examination periods, for JPMorgan Chase for the years 2001 and 2002, and for Bank One and its predecessor entities for various periods from 1996 through 1999.
For years prior to 2001, refund claims relating to income and credit adjustments, and to tax attribute carrybacks, for JPMorgan Chase and its predecessor entities, including Bank One, either have been or will be filed.
Also, interest rate swap valuations by a Bank One predecessor entity for the years 1990 through 1993 are, and have been, the subject of litigation in both the Tax Court and the U. S.  Court of Appeals.
Deferred income tax expense (benefit) results from differences between assets and liabilities measured for financial reporting and for income-tax return purposes.
The significant components of deferred tax assets and liabilities are reflected in the following table.
## Table 2 ##
A valuation allowance has been recorded in accordance with SFAS 109, primarily relating to capital losses associated with certain portfolio investments.
## Table 3 ##
(a) Revenue is composed of Net interest income and Noninterest revenue.
(b) Expense is composed of Noninterest expense and Provision for credit losses.
Note 34 – Business segments JPMorgan Chase is organized into six major reportable business segments — Investment Bank, Retail Financial Services, Card Services, Commercial Banking, Treasury & Securities Services and Asset Management, as well as a Corporate segment.
The segments are based upon the products and services provided or the type of customer served, and they reflect the manner in which financial information is currently evaluated by management.
Results of these lines of business are presented on a managed basis.
For a definition of managed basis, see Explanation and Reconciliation of the Firm’s use of non-GAAP financial measures, on pages 36–37 of this Annual Report.
For a further discussion concerning JPMorgan Chase’s business segments, see Business segment results on pages 38–39 of this Annual Report.
Business segment financial disclosures Capital allocation changes Effective January 1, 2006, the Firm refined its methodology for allocating capital (i. e. , equity) to the business segments.
As a result of this refinement, RFS, CS, CB, TSS and AM have higher amounts of capital allocated to them commencing in the first quarter of 2006.
The revised methodology considers for each line of business, among other things, goodwill associated with such business segment’s acquisitions since the Merger.
In management’s view, the revised methodology assigns responsibility to the lines of business to generate returns on the amount of capital supporting acquisition-related goodwill.
As part of this refinement in the capital allocation methodology, the Firm assigned to the Corporate segment an amount of equity capital equal to the then-current book value of goodwill from and prior to the Merger.
As prior periods have not been revised to reflect the new capital allocations, capital allocated to the respective lines of business for 2005 is not comparable to subsequent periods and certain business metrics, such as return on common equity, are not comparable to the current presentation.
The Firm may revise its equity capital allocation methodology again in the future.
Discontinued operations As a result of the transaction with The Bank of New York, selected corporate trust businesses have been transferred from TSS to the Corporate segment and reported in discontinued operations for all periods reported.

Tables referenced above, in order (Table 0 first):
<table><tr><td>Year ended December 31,(inmillions)</td><td>2007</td><td>2006</td></tr><tr><td>Balance at beginning of period after valuation allowance</td><td>$7,546</td><td>$6,452</td></tr><tr><td>Cumulative effect of change in accounting principle</td><td>—</td><td>230</td></tr><tr><td>Fair value at beginning of period</td><td>7,546</td><td>6,682</td></tr><tr><td>Originations of MSRs</td><td>2,335</td><td>1,512</td></tr><tr><td>Purchase of MSRs</td><td>798</td><td>627</td></tr><tr><td>Total additions</td><td>3,133</td><td>2,139</td></tr><tr><td>Change in valuation due to inputs and assumptions<sup>(a)</sup></td><td>-516</td><td>165</td></tr><tr><td>Other changes in fair value<sup>(b)</sup></td><td>-1,531</td><td>-1,440</td></tr><tr><td>Total change in fair value</td><td>-2,047</td><td>-1,275</td></tr><tr><td>Fair value at December 31</td><td>$8,632</td><td>$7,546</td></tr><tr><td>Change in unrealized (losses) gains included in income related to MSRs held at December 31</td><td>$-516</td><td>NA</td></tr></table>
<table><tr><td>Balance at January 1, 2007</td><td>$4,677</td></tr><tr><td>Increases based on tax positions related to the current period</td><td>434</td></tr><tr><td>Decreases based on tax positions related to the current period</td><td>-241</td></tr><tr><td>Increases based on tax positions related to prior periods</td><td>903</td></tr><tr><td>Decreases based on tax positions related to prior periods</td><td>-791</td></tr><tr><td>Decreases related to settlements with taxing authorities</td><td>-158</td></tr><tr><td>Decreases related to a lapse of applicable statute of limitations</td><td>-13</td></tr><tr><td> Balance at December 31, 2007</td><td>$4,811</td></tr></table>
<table><tr><td>December 31, (in millions)</td><td> 2007</td><td>2006</td></tr><tr><td> Deferred tax assets</td><td></td><td></td></tr><tr><td>Allowance for loan losses</td><td>$3,800</td><td>$2,910</td></tr><tr><td>Allowance for other than loan losses</td><td>3,635</td><td>3,533</td></tr><tr><td>Employee benefits</td><td>3,391</td><td>5,175</td></tr><tr><td>Non-U.S. operations</td><td>285</td><td>566</td></tr><tr><td>Fair value adjustments</td><td>—</td><td>427</td></tr><tr><td> Gross deferred tax assets</td><td>$11,111</td><td>$12,611</td></tr><tr><td> Deferred tax liabilities</td><td></td><td></td></tr><tr><td>Depreciation and amortization</td><td>$2,966</td><td>$3,668</td></tr><tr><td>Leasing transactions</td><td>2,304</td><td>2,675</td></tr><tr><td>Non-U.S. operations</td><td>1,790</td><td>1,435</td></tr><tr><td>Fair value adjustments</td><td>570</td><td>—</td></tr><tr><td>Fee income</td><td>548</td><td>1,216</td></tr><tr><td>Other, net</td><td>207</td><td>78</td></tr><tr><td> Gross deferred tax liabilities</td><td>$8,385</td><td>$9,072</td></tr><tr><td>Valuation allowance</td><td>$220</td><td>$210</td></tr><tr><td> Net deferred tax asset</td><td>$2,506</td><td>$3,329</td></tr></table>
<table><tr><td>Year ended December 31, (in millions)</td><td>Revenue<sup>(a)</sup></td><td>Expense<sup>(b)</sup></td><td>Income from continuing operations before income taxes</td><td>Net income</td></tr><tr><td> 2007</td><td></td><td></td><td></td><td></td></tr><tr><td>Europe/Middle East and Africa</td><td>$12,070</td><td>$8,445</td><td> $ 3,625</td><td>$2,585</td></tr><tr><td>Asia and Pacific</td><td>4,730</td><td>3,117</td><td> 1,613</td><td>945</td></tr><tr><td>Latin America and the Caribbean</td><td>2,028</td><td>975</td><td> 1,053</td><td>630</td></tr><tr><td>Other</td><td>407</td><td>289</td><td> 118</td><td>79</td></tr><tr><td> Total international</td><td>19,235</td><td>12,826</td><td> 6,409</td><td>4,239</td></tr><tr><td>Total U.S.</td><td>52,137</td><td>35,741</td><td> 16,396</td><td>11,126</td></tr><tr><td> Total</td><td>$71,372</td><td>$48,567</td><td> $ 22,805</td><td>$15,365</td></tr><tr><td> 2006</td><td></td><td></td><td></td><td></td></tr><tr><td>Europe/Middle East and Africa</td><td>$11,342</td><td>$7,471</td><td>$ 3,871</td><td>$2,774</td></tr><tr><td>Asia and Pacific</td><td>3,227</td><td>2,649</td><td>578</td><td>400</td></tr><tr><td>Latin America and the Caribbean</td><td>1,342</td><td>820</td><td>522</td><td>333</td></tr><tr><td>Other</td><td>381</td><td>240</td><td>141</td><td>90</td></tr><tr><td> Total international</td><td>16,292</td><td>11,180</td><td>5,112</td><td>3,597</td></tr><tr><td>Total U.S.</td><td>45,707</td><td>30,933</td><td>14,774</td><td>10,847</td></tr><tr><td> Total</td><td>$61,999</td><td>$42,113</td><td>$ 19,886</td><td>$14,444</td></tr><tr><td> 2005</td><td></td><td></td><td></td><td></td></tr><tr><td>Europe/Middle East and Africa</td><td>$7,795</td><td>$5,625</td><td>$ 2,170</td><td>$1,547</td></tr><tr><td>Asia and Pacific</td><td>2,857</td><td>2,075</td><td>782</td><td>509</td></tr><tr><td>Latin America and the Caribbean</td><td>973</td><td>506</td><td>467</td><td>285</td></tr><tr><td>Other</td><td>165</td><td>89</td><td>76</td><td>44</td></tr><tr><td> Total international</td><td>11,790</td><td>8,295</td><td>3,495</td><td>2,385</td></tr><tr><td>Total U.S.</td><td>42,458</td><td>34,114</td><td>8,344</td><td>6,098</td></tr><tr><td> Total</td><td>$54,248</td><td>$42,409</td><td>$ 11,839</td><td>$8,483</td></tr></table>

Question: What is the average amount of Other changes in fair value of 2006, and Balance at January 1, 2007 ?
Answer: 3058.5
Reasoning program: add(1440.0,4677.0), divide(#0,const_2)