Recoverability of goodwill is measured at the reporting unit level and begins with a qualitative assessment to determine if it is more likely than not that the fair value of each reporting unit is less than its carrying amount as a basis for determining whether it is necessary to perform the two-step goodwill impairment test prescribed by GAAP.
For those reporting units where it is required, the first step compares the carrying amount of the reporting unit to its estimated fair value.
If the estimated fair value of a reporting unit exceeds its carrying amount, goodwill of the reporting unit is not impaired and the second step of the impairment test is not necessary.
To the extent that the carrying value of the reporting unit exceeds its estimated fair value, a second step is performed, wherein the reporting unit's carrying value of goodwill is compared to the implied fair value of goodwill.
To the extent that the carrying value exceeds the implied fair value, impairment exists and must be recognized.
The calculation of estimated fair value is based on two valuation techniques, a discounted cash flow model (income approach) and a market adjusted multiple of earnings and revenues (market approach), with each method being weighted in the calculation.
The implied fair value of goodwill is determined in the same manner as the amount of goodwill recognized in a business combination.
The estimated fair value of the reporting unit is allocated to all of the assets and liabilities of the reporting unit (including any unrecognized intangible assets) as if the reporting unit had been acquired in a business combination and the fair value of the reporting unit, as determined in the first step of the goodwill impairment test, was the price paid to acquire that reporting unit.
Recoverability of other intangible assets with indefinite useful lives (i. e.  Trademarks) is determined on a relief from royalty methodology (income approach), which is based on the implied royalty paid, at an appropriate discount rate, to license the use of an asset rather than owning the asset.
The present value of the after-tax cost savings (i. e.  royalty relief) indicates the estimated fair value of the asset.
Any excess of the carrying value over the estimated fair value is recognized as an impairment loss equal to that excess.
Intangible assets such as patents, customer-related intangible assets and other intangible assets with finite useful lives are amortized on a straight-line basis over their estimated economic lives.
The weighted-average useful lives approximate the following:
## Table 0 ##
Recoverability of intangible assets with finite useful lives is assessed in the same manner as property, plant and equipment as described above.
Income Taxes: For purposes of the Company’s Consolidated Financial Statements for periods prior to the Spin-off, income tax expense has been recorded as if the Company filed tax returns on a stand-alone basis separate from Ingersoll Rand.
This separate return methodology applies the accounting guidance for income taxes to the stand-alone financial statements as if the Company was a stand-alone enterprise for the periods prior to the Spin-off.
Therefore, cash tax payments and items of current and deferred taxes may not be reflective of the Company’s actual tax balances prior to or subsequent to the Spin-off.
Cash paid for income taxes for the year ended December 31, 2015 was $80.6 million.
The income tax accounts reflected in the Consolidated Balance Sheets as of December 31, 2015 and 2014 include income taxes payable and deferred taxes allocated to the Company at the time of the Spin-off.
The calculation of the Company’s income taxes involves considerable judgment and the use of both estimates and allocations.
Deferred tax assets and liabilities are determined based on temporary differences between financial reporting and tax bases of assets and liabilities, applying enacted tax rates expected to be in effect for the year in which the differences are expected to reverse.
The Company recognizes future tax benefits, such as net operating losses and tax credits, to the extent that realizing these benefits is considered in its judgment to be more likely than not.
The Company regularly reviews the recoverability of its deferred tax assets considering its historic profitability, projected future taxable income, timing of the reversals of existing temporary differences and the feasibility of its tax planning strategies.
Where appropriate, the Company records a valuation allowance with respect to a future tax benefit.
Product Warranties: Standard product warranty accruals are recorded at the time of sale and are estimated based upon product warranty terms and historical experience.
The Company assesses the adequacy of its liabilities and will make adjustments as necessary based on known or anticipated warranty claims, or as new information becomes available.
Principal Financial Group, Inc.  Notes to Consolidated Financial Statements — (continued) 1.
Nature of Operations and Significant Accounting Policies — (continued) Goodwill and Other Intangibles Goodwill and other intangible assets include the cost of acquired subsidiaries in excess of the fair value of the net tangible assets recorded in connection with acquisitions.
Goodwill and indefinite-lived intangible assets are not amortized.
Rather, they are tested for impairment during the fourth quarter each year, or more frequently if events or changes in circumstances indicate that the asset might be impaired.
Goodwill is tested at the reporting unit level to which it was assigned.
A reporting unit is an operating segment or a business one level below that operating segment, if financial information is prepared and regularly reviewed by management at that level.
Once goodwill has been assigned to a reporting unit, it is no longer associated with a particular acquisition; therefore, all of the activities within a reporting unit, whether acquired or organically grown, are available to support the goodwill value.
Impairment testing for indefinite-lived intangible assets consists of a comparison of the fair value of the intangible asset with its carrying value.
Intangible assets with a finite useful life are amortized as related benefits emerge and are reviewed periodically for indicators of impairment in value.
If facts and circumstances suggest possible impairment, the sum of the estimated undiscounted future cash flows expected to result from the use of the asset is compared to the current carrying value of the asset.
If the undiscounted future cash flows are less than the carrying value, an impairment loss is recognized for the excess of the carrying amount of assets over their fair value.
Earnings Per Common Share Basic earnings per common share is calculated by dividing income available to common stockholders by the weighted-average number of common shares outstanding for the period and excludes the dilutive effect of equity awards.
Diluted earnings per common share reflects the potential dilution that could occur if dilutive securities, such as options and non-vested stock grants, were exercised or resulted in the issuance of common stock.2.
Goodwill and Other Intangible Assets Goodwill The changes in the carrying amount of goodwill reported in our segments were as follows:
## Table 1 ##
On September 30, 2010, we announced our decision to exit the group medical insurance business.
This event constituted a substantive change in circumstances that would more likely than not reduce the fair value of our group medical insurance reporting unit below its carrying amount.
Accordingly, we performed an interim goodwill impairment test as of September 30, 2010.
As a result of the shortened period of projected cash flows, we determined that the goodwill related to this reporting unit within our Corporate operating segment was impaired and it was written down to a value of zero.
We recorded a $43.6 million pre-tax impairment loss as an operating expense in the consolidated statements of operations during the year ended December 31, 2010.
Principal Financial Group, Inc.  Notes to Consolidated Financial Statements — (continued) 3.
Variable Interest Entities — (continued) We did not provide financial or other support to investees designated as VIEs for the years ended December 31, 2010 and 2009.
Unconsolidated Variable Interest Entities Invested Securities We hold a variable interest in a number of VIEs where we are not the primary beneficiary.
Our investments in securities issued by these VIEs are reported in fixed maturities, available-for-sale and fixed maturities, trading in the consolidated statements of financial position and are described below.
VIEs include CMBS, residential mortgage-backed securities and asset-backed securities.
All of these entities were deemed VIEs upon the removal of the QSPE scope exception because the equity within these entities is insufficient to sustain them.
We currently are not the primary beneficiary in any of the entities within these categories of investments.
This determination was based primarily on the fact we do not own the class of security that controls the unilateral right to replace the special servicer or equivalent function.
As previously discussed, we invest in several types of collateralized private investment vehicles, which are VIEs.
These include cash and synthetic structures that we do not manage.
We are currently not the primary beneficiary of these collateralized private investment vehicles primarily because we do not control the economic performance of the entities and were not involved with the design of the entities.
We have invested in various VIE trusts as a debt holder.
All of these entities are classified as VIEs due to insufficient equity to sustain them.
Prior to January 1, 2010, we had performed a quantitative analysis and concluded that although we held a significant variable interest in these entities we were not the primary beneficiary due to lack of majority of the risk of loss or because they were scoped out as a QSPE.
Beginning January 1, 2010, we concluded we are not the primary beneficiary primarily because we do not control the economic performance of the entities and were not involved with the design of the entities.
Prior to January 1, 2010, we were only required to disclose information about carrying value and maximum loss exposure for our significant unconsolidated VIEs.
The carrying value and maximum loss exposure for our unconsolidated VIEs as of December 31, 2010, and for our significant unconsolidated VIEs as of December 31, 2009, were as follows:
## Table 2 ##
(1) Our risk of loss is limited to our initial investment measured at amortized cost for fixed maturities, available-for-sale and to fair value for our fixed maturities, trading.
Sponsored Investment Funds We are the investment manager for certain money market mutual funds that are deemed to be VIEs.
We are not the primary beneficiary of these VIEs since our involvement is limited primarily to being a service provider, and our variable interest does not absorb the majority of the variability of the entities’ net assets.
As of December 31, 2010, these VIEs held $1.7 billion in total assets.
During 2010, we chose to contribute $3.2 million to these VIEs for competitive reasons and have no contractual obligation to further contribute to the funds.
We provide asset management and other services to certain investment structures that are considered VIEs as we generally earn management fees and in some instances performance based fees.
We are not the primary beneficiary of these entities as we do not have the obligation to absorb losses of the entities that could be potentially significant to the VIE or the right to receive benefits from these entities that could be potentially significant.
Net investment income decreased primarily due to lower inflation-based investment returns related to deflation in Chile during 2009, lower yields on floating rate investments supporting floating rate liabilities, and a decrease in average invested assets.
For additional information, see ‘‘Investments — Investment Results.
’’ Net realized capital gains (losses) can be volatile due to mark-to-market adjustments of certain invested assets, other than temporary impairments of invested assets and our decision to sell invested assets.
Net realized capital losses decreased primarily due to mark-to-market gains versus losses on fixed maturities and equity securities classified as trading and higher gains on sales of fixed maturities.
For additional information, see ‘‘Investments — Investment Results.
’’ Total Expenses Benefits, claims and settlement expenses decreased $538.1 million for our Retirement and Investor Services segment, primarily due to a decrease in our investment only business resulting from our decision to scale back this business and lower variable crediting rates.
Also contributing to the decline within the segment was a decrease in the change in reserves resulting from lower sales of annuities with life contingencies in our full service payout and individual annuities businesses.
In addition, benefits, claims and settlement expenses decreased $257.4 million for our Principal International segment, primarily due to lower interest crediting rates to customers in Chile, which were impacted by deflation, and the weakening of the Chilean peso against the U. S.  dollar.
Despite a $177.0 million increase in employee defined benefit pension and other postretirement benefit costs, operating expenses (excluding the impacts of DPAC and commissions) for our organization decreased as a result of company-wide expense savings initiatives.
Retirement and Investor Services operating expenses decreased $358.5 million, primarily due to a decrease in DPAC amortization related to favorable true-up impacts from equity markets in 2009 compared to unfavorable true-up impacts from equity markets in 2008.
In addition, lower commission expense and fees paid to advisors stemming from a decrease in average account values in our Principal Funds business contributed to a decline in segment operating expenses.
Furthermore, operating expenses decreased $115.6 million for the U. S.  Insurance Solutions segment, primarily due to lower DPAC amortization and lower non-deferred sales-related expenses in our individual life insurance business.
Income Taxes The effective income tax rates were 13% and 1% for the years ended December 31, 2009 and 2008, respectively.
The effective income tax rate for the year ended December 31, 2009, was lower than the U. S.  statutory rate primarily due to income tax deductions allowed for corporate dividends received, taxes on our share of earnings generated from equity method investments reflected in net investment income and the interest exclusion from taxable income.
The effective income tax rate for the year ended December 31, 2008, was lower than the U. S.  statutory rate primarily due to income tax deductions allowed for corporate dividends received, interest exclusion from taxable income and additional U. S.  foreign tax credits resulting from the second quarter 2008 enactment of legislation to increase the Brazilian tax rate.
The effective income tax rate increased to 13% from 1% for the years ended December 31, 2009 and 2008, respectively, primarily due to a decrease in our net realized capital losses with no proportionate change in permanent items and additional U. S.  foreign tax credits reflected in 2008 resulting from the Brazilian tax rate increase.
The net increase in deferred tax liabilities associated with the 2008 enacted Brazilian income tax rate is reflected in net investment income because the equity method of accounting is applied to our Brazilian operations; however, the benefit from additional U. S.  foreign tax credits is reflected in income tax expense.
Results of Operations by Segment For results of operations by segment see Item 8.
‘‘Financial Statements and Supplementary Data, Notes to Consolidated Financial Statements, Note 16, Segment Information.
’’ Retirement and Investor Services Segment Retirement and Investor Services Trends Account values are a key indicator of earnings growth for the segment, as account values are the base by which the segment generates its fee and spread-based profits.
Net cash flow and market performance are the two main drivers of account value growth.
Net cash flow reflects the segment’s ability to attract and retain client deposits.
Market performance reflects not only the equity market performance, but also the investment performance of fixed income investments supporting our spread business.
The percentage growth in earnings of the segment should generally track the percentage growth in account values.
This trend may vary due to changes in business and/or product mix.
The following table presents the Retirement and Investor Services account value rollforward for the years indicated:

<table><tr><td>Customer relationships</td><td>25</td><td>years</td></tr><tr><td>Trademarks</td><td>25</td><td>years</td></tr><tr><td>Completed technology/patents</td><td>10</td><td>years</td></tr><tr><td>Other</td><td>25</td><td>years</td></tr></table>
<table><tr><td> </td><td> Retirement and Investor Services</td><td> Principal Global Investors</td><td>Principal International</td><td> U.S. Insurance Solutions</td><td>Corporate</td><td>Consolidated</td></tr><tr><td> </td><td colspan="6">(in millions)</td></tr><tr><td> Balances at January 1, 2009</td><td>$72.6</td><td>$169.0</td><td>$45.4</td><td>$43.4</td><td>$45.1</td><td>$375.5</td></tr><tr><td>Foreign currency translation</td><td>—</td><td>—</td><td>10.9</td><td>—</td><td>—</td><td>10.9</td></tr><tr><td> Balances at December 31, 2009</td><td>72.6</td><td>169.0</td><td>56.3</td><td>43.4</td><td>45.1</td><td>386.4</td></tr><tr><td>Impairment</td><td>—</td><td>—</td><td>—</td><td>—</td><td>-43.6</td><td>-43.6</td></tr><tr><td>Foreign currency translation</td><td>—</td><td>—</td><td>4.2</td><td>—</td><td>—</td><td>4.2</td></tr><tr><td>Other</td><td>—</td><td>—</td><td>-1.6</td><td>—</td><td>—</td><td>-1.6</td></tr><tr><td> Balances at December 31, 2010</td><td>$72.6</td><td>$169.0</td><td>$58.9</td><td>$43.4</td><td>$1.5</td><td>$345.4</td></tr></table>
<table><tr><td> </td><td> Asset carrying value</td><td> Maximum exposure to loss -1</td></tr><tr><td> </td><td colspan="2"><i>(in millions)</i> </td></tr><tr><td> December 31, 2010</td><td></td><td></td></tr><tr><td>Fixed maturities, available-for-sale:</td><td></td><td></td></tr><tr><td>Corporate</td><td>$429.0</td><td>$367.7</td></tr><tr><td>Residential mortgage-backed securities</td><td>3,196.2</td><td>3,077.9</td></tr><tr><td>Commercial mortgage-backed securities</td><td>3,842.2</td><td>4,424.9</td></tr><tr><td>Collateralized debt obligations</td><td>293.0</td><td>380.5</td></tr><tr><td>Other debt obligations</td><td>3,114.1</td><td>3,184.9</td></tr><tr><td>Fixed maturities, trading:</td><td></td><td></td></tr><tr><td>Residential mortgage-backed securities</td><td>215.5</td><td>215.5</td></tr><tr><td>Commercial mortgage-backed securities</td><td>5.1</td><td>5.1</td></tr><tr><td>Collateralized debt obligations</td><td>87.2</td><td>87.2</td></tr><tr><td>Other debt obligations</td><td>118.8</td><td>118.8</td></tr><tr><td> December 31, 2009</td><td></td><td></td></tr><tr><td>Fixed maturities, available-for-sale:</td><td></td><td></td></tr><tr><td>Corporate</td><td>$162.8</td><td>$144.2</td></tr></table>

Question: what is the difference between the weighted average useful lives of trademarks and patents , in number of years?\\n