## Table 0 ##
The risk-free interest rate is based on the zero-coupon U. S.  Treasury yield curve in effect at the time of grant.
The expected life computation is derived from historical exercise patterns and anticipated future patterns.
Expected volatilities are based on historical volatility of our stock.
Restricted Stock Plans Restricted stock units are granted at the discretion of the compensation committee of the board of directors.
We granted 3,274,358, 3,251,017 and 3,457,590 time-based and performance-based restricted stock units during the years ended December 31, 2017, 2016 and 2015, respectively, including 2,364,288, 2,325,985 and 1,871,785 time-based restricted stock units during the years ended December 31, 2017, 2016 and 2015, respectively.
The grant date fair value of each award is based on the closing stock price at the date of grant.
The fair value of the time-based restricted stock units on the date of grant is recognized as expense ratably over the vesting period, which is typically three years, net of forfeitures.
Granted but unvested shares are generally forfeited upon termination of employment.
When restricted stock is forfeited, compensation costs previously recognized for unvested shares are reversed.
Until the shares vest and are issued, the participants have no voting or dividend rights and the shares may not be sold, assigned, transferred, pledged or otherwise encumbered.
Unvested restricted stock earns dividend equivalents which are paid in cash on the vesting date.
We recognize compensation costs, net of forfeitures, using an accelerated attribution method over the vesting period for awards with performance conditions.
Compensation costs for such awards are recognized only if it is probable that the condition will be satisfied.
If we initially determine that it is not probable that the performance condition will be satisfied and later determine that it is probable that the performance condition will be satisfied, or vice versa, the effect of the change in estimate is accounted for in the period of change by recording a cumulative catch-up adjustment to retroactively apply the new estimate.
We recognize the remaining compensation costs over the remaining vesting period.
Our compensation committee, pursuant to the terms of the equity plans and the authority delegated to it by our board of directors, can make equitable adjustments to the performance condition in recognition of unusual or non-recurring events.
In January 2017, we reserved a maximum of 1,534,218 restricted shares for potential issuance as performance-based restricted shares for certain of our employees.
These restricted shares were subject to a market condition that could have reduced the number of shares that were awarded if our 2017 total shareholder return fell below that of the 2017 return of the S&P 500 Index and if we achieved above target financial performance level.
Our total shareholder return for the year ended December 31, 2017 was higher than the 2017 return of the S&P 500 Index.
Therefore, no share reduction was required.
Based on our actual 2017 financial performance as compared to the 2017 financial performance level thresholds, 767,109 restricted shares were awarded, which resulted in $43 million in compensation expenses that will be expensed over the three-year accelerated vesting period, including $26 million that was expensed during the year ended December 31, 2017.
The grant date fair values of the awards with a market condition were estimated based on our stock price on the grant date, the valuation of historical awards with market conditions, the relatively low likelihood that the market condition will affect the number of shares granted (as the market condition only affects shares granted in excess of certain financial performance targets), and our expectation of achieving the financial performance targets.
The grant date fair value of the awards, when considering the impact of the market condition on fair value, was determined to not be materially different from our stock price on the respective grant dates.
Restricted shares are used as an incentive to attract and retain qualified employees and to increase shareholder returns with actual performance linked to both short and long-term shareholder return.
Our equity plans include a change in control provision that may accelerate vesting on both the time-based and performance-based restricted shares if the awards are not assumed by an acquirer in the case of a change in control.
The following is a summary of the nonvested restricted shares under all plans discussed above for the years ended December 31, 2017, 2016 and 2015:
## Table 1 ##
(a) Includes the impact of National City, which we acquired on December 31, 2008.
(b) Includes the impact of National City except for the following Selected Ratios: Noninterest income to total revenue, Efficiency, Net interest margin, Return on Average common shareholders’ equity, Return on Average assets, Dividend payout, and Average common shareholders’ equity to average assets.
(c) Includes our investment in BlackRock beginning with the 2006 balance.
BlackRock was a consolidated entity at December 31, 2005.
(d) Includes long-term borrowings of $26.3 billion, $33.6 billion, $12.6 billion, $6.6 billion and $6.8 billion for 2009, 2008, 2007, 2006 and 2005, respectively.
Borrowings which mature more than one year after December 31, 2009 are considered to be long-term.
(e) Assets under management at December 31, 2005 include BlackRock’s assets under management.
We deconsolidated BlackRock effective September 29, 2006.
(f) Calculated as taxable-equivalent net interest income divided by average earning assets.
The interest income earned on certain earning assets is completely or partially exempt from federal income tax.
As such, these tax-exempt instruments typically yield lower returns than taxable investments.
To provide more meaningful comparisons of margins for all earning assets, we use net interest income on a taxable-equivalent basis in calculating net interest margin by increasing the interest income earned on tax-exempt assets to make it fully equivalent to interest income earned on taxable investments.
This adjustment is not permitted under GAAP on the Consolidated Income Statement.
The taxableequivalent adjustments to net interest income for the years 2009, 2008, 2007, 2006 and 2005 were $65 million, $36 million, $27 million, $25 million and $33 million, respectively
Market Street Commitments by Credit Rating (a)
## Table 2 ##
(a) The majority of our facilities are not explicitly rated by the rating agencies.
All facilities are structured to meet rating agency standards for applicable rating levels.
We evaluated the design of Market Street, its capital structure, the Note, and relationships among the variable interest holders.
Based on this analysis and under accounting guidance effective during 2009 and 2008, we are not the primary beneficiary and therefore the assets and liabilities of Market Street are not included on our Consolidated Balance Sheet.
We considered changes to the variable interest holders (such as new expected loss note investors and changes to programlevel credit enhancement providers), terms of expected loss notes, and new types of risks related to Market Street as reconsideration events.
We reviewed the activities of Market Street on at least a quarterly basis to determine if a reconsideration event has occurred.
Tax Credit Investments We make certain equity investments in various limited partnerships or limited liability companies (LLCs) that sponsor affordable housing projects utilizing the Low Income Housing Tax Credit (LIHTC) pursuant to Sections 42 and 47 of the Internal Revenue Code.
The purpose of these investments is to achieve a satisfactory return on capital, to facilitate the sale of additional affordable housing product offerings and to assist us in achieving goals associated with the Community Reinvestment Act.
The primary activities of the investments include the identification, development and operation of multi-family housing that is leased to qualifying residential tenants.
Generally, these types of investments are funded through a combination of debt and equity.
We typically invest in these partnerships as a limited partner or non-managing member.
Also, we are a national syndicator of affordable housing equity (together with the investments described above, the “LIHTC investments”).
In these syndication transactions, we create funds in which our subsidiaries are the general partner or managing member and sell limited partnership or non-managing member interests to third parties, and in some cases may also purchase a limited partnership or non-managing member interest in the fund.
The purpose of this business is to generate income from the syndication of these funds, generate servicing fees by managing the funds, and earn tax credits to reduce our tax liability.
General partner or managing member activities include selecting, evaluating, structuring, negotiating, and closing the fund investments in operating limited partnerships, as well as oversight of the ongoing operations of the fund portfolio.
We evaluate our interests and third party interests in the limited partnerships/LLCs in determining whether we are the primary beneficiary.
The primary beneficiary determination is based on which party absorbs a majority of the variability.
The primary sources of variability in LIHTC investments are the tax credits, tax benefits due to passive losses on the investments and development and operating cash flows.
We have consolidated LIHTC investments in which we absorb a majority of the variability and thus are considered the primary beneficiary.
The assets are primarily included in Equity investments and Other assets on our Consolidated Balance Sheet with the liabilities classified in Other liabilities and third party investors’ interests included in the Equity section as Noncontrolling interests.
Neither creditors nor equity investors in the LIHTC investments have any recourse to our general credit.
The consolidated aggregate assets and liabilities of these LIHTC investments are provided in the Consolidated VIEs – PNC Is Primary Beneficiary table and reflected in the “Other” business segment.
We also have LIHTC investments in which we are not the primary beneficiary, but are considered to have a significant variable interest based on our interests in the partnership/LLC.
These investments are disclosed in the Non-Consolidated VIEs – Significant Variable Interests table.
The table also reflects our maximum exposure to loss.
Our maximum exposure to loss is equal to our legally binding equity commitments adjusted for recorded impairment and partnership results.
We use the equity and cost methods to account for our investment in these entities with the investments reflected in Equity investments on our Consolidated Balance Sheet.
In addition, we increase our recognized investments and recognize a liability for all legally binding unfunded equity commitments.
These liabilities are reflected in Other liabilities on our Consolidated Balance Sheet.
Credit Risk Transfer Transaction National City Bank, (a former PNC subsidiary which merged into PNC Bank, N. A.  in November 2009) sponsored a special purpose entity (SPE) and concurrently entered into a credit risk transfer agreement with an independent third party to mitigate credit losses on a pool of nonconforming mortgage loans originated by its former First Franklin business unit.
The SPE was formed with a small equity contribution and was structured as a bankruptcy-remote entity so that its creditors have no recourse to us.
In exchange for a perfected security interest in the cash flows of the nonconforming mortgage loans, the SPE issued to us asset-backed securities in the form of senior, mezzanine, and subordinated equity notes.
The SPE was deemed to be a VIE as its equity was not sufficient to finance its activities.
We were determined to be the primary beneficiary of the SPE as we would absorb the majority of the expected losses of the SPE through our holding of the asset-backed securities.
Accordingly, this SPE was consolidated and all of the entity’s assets, liabilities, and

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td colspan="3">Year Ended December 31,</td></tr><tr><td>Assumptions</td><td>2017</td><td>2016</td><td>2015</td></tr><tr><td>Risk-free interest rate</td><td>1.84%</td><td>1.51%</td><td>1.08%</td></tr><tr><td>Expected life in years</td><td>5.0</td><td>5.0</td><td>5.0</td></tr><tr><td>Expected volatility</td><td>21%</td><td>24%</td><td>24%</td></tr><tr><td>Expected dividend yield</td><td>1.40%</td><td>1.36%</td><td>1.25%</td></tr><tr><td>Estimated fair value of options granted per share</td><td>$10.50</td><td>$9.88</td><td>$8.19</td></tr></table>
<table><tr><td></td><td colspan="5">At or for the year ended December 31</td></tr><tr><td>Dollars in millions, except as noted</td><td>2009 (a)</td><td>2008 (b)</td><td>2007</td><td>2006</td><td>2005</td></tr><tr><td> BALANCESHEETHIGHLIGHTS</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Assets</td><td>$269,863</td><td>$291,081</td><td>$138,920</td><td>$101,820</td><td>$91,954</td></tr><tr><td>Loans</td><td>157,543</td><td>175,489</td><td>68,319</td><td>50,105</td><td>49,101</td></tr><tr><td>Allowance for loan and lease losses</td><td>5,072</td><td>3,917</td><td>830</td><td>560</td><td>596</td></tr><tr><td>Interest-earning deposits with banks</td><td>4,488</td><td>14,859</td><td>346</td><td>339</td><td>669</td></tr><tr><td>Investment securities</td><td>56,027</td><td>43,473</td><td>30,225</td><td>23,191</td><td>20,710</td></tr><tr><td>Loans held for sale</td><td>2,539</td><td>4,366</td><td>3,927</td><td>2,366</td><td>2,449</td></tr><tr><td>Goodwill and other intangible assets</td><td>12,909</td><td>11,688</td><td>9,551</td><td>4,043</td><td>4,466</td></tr><tr><td>Equity investments (c)</td><td>10,254</td><td>8,554</td><td>6,045</td><td>5,330</td><td>1,323</td></tr><tr><td>Noninterest-bearing deposits</td><td>44,384</td><td>37,148</td><td>19,440</td><td>16,070</td><td>14,988</td></tr><tr><td>Interest-bearing deposits</td><td>142,538</td><td>155,717</td><td>63,256</td><td>50,231</td><td>45,287</td></tr><tr><td>Total deposits</td><td>186,922</td><td>192,865</td><td>82,696</td><td>66,301</td><td>60,275</td></tr><tr><td>Borrowed funds (d)</td><td>39,261</td><td>52,240</td><td>30,931</td><td>15,028</td><td>16,897</td></tr><tr><td>Shareholders’ equity</td><td>29,942</td><td>25,422</td><td>14,854</td><td>10,788</td><td>8,563</td></tr><tr><td>Common shareholders’ equity</td><td>22,011</td><td>17,490</td><td>14,847</td><td>10,781</td><td>8,555</td></tr><tr><td> ASSETSUNDERADMINISTRATION(billions)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Discretionary assets under management (e)</td><td>$103</td><td>$103</td><td>$74</td><td>$55</td><td>$495</td></tr><tr><td>Nondiscretionary assets under management</td><td>102</td><td>125</td><td>112</td><td>85</td><td>83</td></tr><tr><td>Total assets under administration</td><td>$205</td><td>$228</td><td>$186</td><td>$140</td><td>$578</td></tr><tr><td> SELECTEDRATIOS</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>From continuing operations</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Noninterest income to total revenue</td><td>44</td><td>39</td><td>50</td><td>70</td><td>60</td></tr><tr><td>Efficiency</td><td>56</td><td>59</td><td>62</td><td>49</td><td>67</td></tr><tr><td>From net income</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Net interest margin (f)</td><td>3.82%</td><td>3.37%</td><td>3.00%</td><td>2.92%</td><td>3.00%</td></tr><tr><td>Return on</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Average common shareholders’ equity</td><td>9.78</td><td>6.52</td><td>10.70</td><td>28.01</td><td>17.00</td></tr><tr><td>Average assets</td><td>.87</td><td>.64</td><td>1.21</td><td>2.74</td><td>1.53</td></tr><tr><td>Loans to deposits</td><td>84</td><td>91</td><td>83</td><td>76</td><td>81</td></tr><tr><td>Dividend payout</td><td>21.4</td><td>104.6</td><td>55.0</td><td>24.4</td><td>43.4</td></tr><tr><td>Tier 1 risk-based</td><td>11.4</td><td>9.7</td><td>6.8</td><td>10.4</td><td>8.3</td></tr><tr><td>Tier 1 common</td><td>6.0</td><td>4.8</td><td>5.4</td><td>8.7</td><td>6.1</td></tr><tr><td>Common shareholders’ equity to total assets</td><td>8.2</td><td>6.0</td><td>10.7</td><td>10.6</td><td>9.3</td></tr><tr><td>Average common shareholders’ equity to average assets</td><td>7.2</td><td>9.6</td><td>11.3</td><td>9.8</td><td>9.0</td></tr><tr><td> SELECTEDSTATISTICS</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Employees</td><td>55,820</td><td>59,595</td><td>28,320</td><td>23,783</td><td>25,348</td></tr><tr><td>Retail Banking branches</td><td>2,512</td><td>2,580</td><td>1,102</td><td>848</td><td>835</td></tr><tr><td>ATMs</td><td>6,473</td><td>6,233</td><td>3,900</td><td>3,581</td><td>3,721</td></tr><tr><td>Residential mortgage servicing portfolio (billions)</td><td>$158</td><td>$187</td><td></td><td></td><td></td></tr><tr><td>Commercial mortgage servicing portfolio (billions)</td><td>$287</td><td>$270</td><td>$243</td><td>$200</td><td>$136</td></tr></table>
<table><tr><td></td><td>December 31, 2009</td><td>December 31,2008</td></tr><tr><td>AAA/Aaa</td><td>14%</td><td>19%</td></tr><tr><td>AA/Aa</td><td>50</td><td>6</td></tr><tr><td>A/A</td><td>34</td><td>72</td></tr><tr><td>BBB/Baa</td><td>2</td><td>3</td></tr><tr><td>Total</td><td>100%</td><td>100%</td></tr></table>

Question: if there were 50 facilities being rated in 2009 , how many were bbb/baa?
Answer: 1
Reasoning program: divide(100,50), divide(#0,#0)