Read the following texts and table with financial data from an S&P 500 earnings report carefully.Based on the question-answer history (if provided), answer the last question. The answer may require mathematical calculation based on the data provided.


republic services , inc . notes to consolidated financial statements 2014 ( continued ) in december 2008 , the board of directors amended and restated the republic services , inc . 2006 incentive stock plan ( formerly known as the allied waste industries , inc . 2006 incentive stock plan ( the 2006 plan ) ) . allied 2019s shareholders approved the 2006 plan in may 2006 . the 2006 plan was amended and restated in december 2008 to reflect republic as the new sponsor of the plan , and that any references to shares of common stock are to shares of common stock of republic , and to adjust outstanding awards and the number of shares available under the plan to reflect the allied acquisition . the 2006 plan , as amended and restated , provided for the grant of non- qualified stock options , incentive stock options , shares of restricted stock , shares of phantom stock , stock bonuses , restricted stock units , stock appreciation rights , performance awards , dividend equivalents , cash awards , or other stock-based awards . awards granted under the 2006 plan prior to december 5 , 2008 became fully vested and nonforfeitable upon the closing of the allied acquisition . no further awards will be made under the 2006 stock options we use a lattice binomial option-pricing model to value our stock option grants . we recognize compensation expense on a straight-line basis over the requisite service period for each separately vesting portion of the award , or to the employee 2019s retirement eligible date , if earlier . expected volatility is based on the weighted average of the most recent one year volatility and a historical rolling average volatility of our stock over the expected life of the option . the risk-free interest rate is based on federal reserve rates in effect for bonds with maturity dates equal to the expected term of the option . we use historical data to estimate future option exercises , forfeitures ( at 3.0% ( 3.0 % ) for each of the periods presented ) and expected life of the options . when appropriate , separate groups of employees that have similar historical exercise behavior are considered separately for valuation purposes . the weighted-average estimated fair values of stock options granted during the years ended december 31 , 2014 , 2013 and 2012 were $ 5.74 , $ 5.27 and $ 4.77 per option , respectively , which were calculated using the following weighted-average assumptions: . <table class='wikitable'><tr><td>1</td><td>-</td><td>2014</td><td>2013</td><td>2012</td></tr><tr><td>2</td><td>expected volatility</td><td>27.5% ( 27.5 % )</td><td>28.9% ( 28.9 % )</td><td>27.8% ( 27.8 % )</td></tr><tr><td>3</td><td>risk-free interest rate</td><td>1.4% ( 1.4 % )</td><td>0.7% ( 0.7 % )</td><td>0.8% ( 0.8 % )</td></tr><tr><td>4</td><td>dividend yield</td><td>3.2% ( 3.2 % )</td><td>3.2% ( 3.2 % )</td><td>3.2% ( 3.2 % )</td></tr><tr><td>5</td><td>expected life ( in years )</td><td>4.6</td><td>4.5</td><td>4.5</td></tr><tr><td>6</td><td>contractual life ( in years )</td><td>7.0</td><td>7.0</td><td>7.0</td></tr></table> .
Question: what was the difference in weighted-average estimated fair values of stock options granted between 2013 and 2014?

0.47