{"pre_text": ["5 .", "stock based compensation overview maa accounts for its stock based employee compensation plans in accordance with accounting standards governing stock based compensation .", "these standards require an entity to measure the cost of employee services received in exchange for an award of an equity instrument based on the award's fair value on the grant date and recognize the cost over the period during which the employee is required to provide service in exchange for the award , which is generally the vesting period .", "any liability awards issued are remeasured at each reporting period .", "maa 2019s stock compensation plans consist of a number of incentives provided to attract and retain independent directors , executive officers and key employees .", "incentives are currently granted under the second amended and restated 2013 stock incentive plan , or the stock plan , which was approved at the 2018 annual meeting of maa shareholders .", "the stock plan allows for the grant of restricted stock and stock options up to 2000000 shares .", "maa believes that such awards better align the interests of its employees with those of its shareholders .", "compensation expense is generally recognized for service based restricted stock awards using the straight-line method over the vesting period of the shares regardless of cliff or ratable vesting distinctions .", "compensation expense for market and performance based restricted stock awards is generally recognized using the accelerated amortization method with each vesting tranche valued as a separate award , with a separate vesting date , consistent with the estimated value of the award at each period end .", "additionally , compensation expense is adjusted for actual forfeitures for all awards in the period that the award was forfeited .", "compensation expense for stock options is generally recognized on a straight-line basis over the requisite service period .", "maa presents stock compensation expense in the consolidated statements of operations in \"general and administrative expenses\" .", "total compensation expense under the stock plan was $ 12.9 million , $ 10.8 million and $ 12.2 million for the years ended december 31 , 2018 , 2017 and 2016 , respectively .", "of these amounts , total compensation expense capitalized was $ 0.5 million , $ 0.2 million and $ 0.7 million for the years ended december 31 , 2018 , 2017 and 2016 , respectively .", "as of december 31 , 2018 , the total unrecognized compensation expense was $ 13.5 million .", "this cost is expected to be recognized over the remaining weighted average period of 1.1 years .", "total cash paid for the settlement of plan shares totaled $ 2.9 million , $ 4.8 million and $ 2.0 million for the years ended december 31 , 2018 , 2017 and 2016 , respectively .", "information concerning grants under the stock plan is provided below .", "restricted stock in general , restricted stock is earned based on either a service condition , performance condition , or market condition , or a combination thereof , and generally vests ratably over a period from 1 year to 5 years .", "service based awards are earned when the employee remains employed over the requisite service period and are valued on the grant date based upon the market price of maa common stock on the date of grant .", "market based awards are earned when maa reaches a specified stock price or specified return on the stock price ( price appreciation plus dividends ) and are valued on the grant date using a monte carlo simulation .", "performance based awards are earned when maa reaches certain operational goals such as funds from operations , or ffo , targets and are valued based upon the market price of maa common stock on the date of grant as well as the probability of reaching the stated targets .", "maa remeasures the fair value of the performance based awards each balance sheet date with adjustments made on a cumulative basis until the award is settled and the final compensation is known .", "the weighted average grant date fair value per share of restricted stock awards granted during the years ended december 31 , 2018 , 2017 and 2016 , was $ 71.85 , $ 84.53 and $ 73.20 , respectively .", "the following is a summary of the key assumptions used in the valuation calculations for market based awards granted during the years ended december 31 , 2018 , 2017 and 2016: ."], "post_text": ["the risk free rate was based on a zero coupon risk-free rate .", "the minimum risk free rate was based on a period of 0.25 years for the years ended december 31 , 2018 , 2017 and 2016 .", "the maximum risk free rate was based on a period of 3 years for the years ended december 31 , 2018 , 2017 and 2016 .", "the dividend yield was based on the closing stock price of maa stock on the ."], "table": [["", "2018", "2017", "2016"], ["risk free rate", "1.61% ( 1.61 % ) - 2.14% ( 2.14 % )", "0.65% ( 0.65 % ) - 1.57% ( 1.57 % )", "0.49% ( 0.49 % ) - 1.27% ( 1.27 % )"], ["dividend yield", "3.884% ( 3.884 % )", "3.573% ( 3.573 % )", "3.634% ( 3.634 % )"], ["volatility", "15.05% ( 15.05 % ) - 17.18% ( 17.18 % )", "20.43% ( 20.43 % ) - 21.85% ( 21.85 % )", "18.41% ( 18.41 % ) - 19.45% ( 19.45 % )"], ["requisite service period", "3 years", "3 years", "3 years"]], "table_ori": [["", "2018", "2017", "2016"], ["Risk free rate", "1.61% - 2.14%", "0.65% - 1.57%", "0.49% - 1.27%"], ["Dividend yield", "3.884%", "3.573%", "3.634%"], ["Volatility", "15.05% - 17.18%", "20.43% - 21.85%", "18.41% - 19.45%"], ["Requisite service period", "3 years", "3 years", "3 years"]]}

Question: considering the year 2018 , what is the average risk-free rate?
Evidence:
table_1: the risk free rate of 2018 is 1.61% ( 1.61 % ) - 2.14% ( 2.14 % ) ; the risk free rate of 2017 is 0.65% ( 0.65 % ) - 1.57% ( 1.57 % ) ; the risk free rate of 2016 is 0.49% ( 0.49 % ) - 1.27% ( 1.27 % ) ;
Program: add(1.61%, 2.14%), divide(#0, const_2)
Answer:
str_answer: 1.875%
exe_answer: 0.01875