How to fetch data into input field using ajax when an item is selected

I want to select a branch code from the option and automatically fill the bank date input from mysql database. I applied ajax and its fetches the data alright but it does not show in the input field unless I check with the inspect element from the browser to see the data was fetched. I want the data appear in the input field. I will be glad you helped. Thanks

The html form

<form method="post" action="">
                <!--=== Table Classes ===-->
                <div class="form-group">
                                    <div class="row">
                                        <div class="col-md-4">
                                            <input type="text" name="pdate" required="required" class="form-control" value="<?php echo date('Y-m-d');?>" readonly=""><span>Login date</span><br>
                                        </div>
                                        <div class="col-md-4">
                                            <select name="branch_code" class=" select2  required form-control" required="required" id="branch_code" >
                                            <option></option>
                                            <?php
                    $tempholder = array();
                    $query = mysql_query("SELECT branch_code FROM users");
                    while($row = mysql_fetch_array($query)) {
                    echo'<option value="'.$row['branch_code'].'" >'.$row['branch_code'].'</option>';
                } 
                    ?>
                                        </select><span>Branch code</span><br>
                                        </div>
                                        <div class="col-md-4">
                                            <input type="text" name="amount" class="form-control" id="w_date" required="required" ><span>Bank date</span><br>
                                        </div>
                                    </div>
                                </div>
                                <hr style="border-color:lightblue;">
                <div class="col-md-12">
                <button type="submit" class="btn btn-default"><i class="fa fa-save"> Save</i></button>
                <button type="reset" class="btn btn-default"><i class="fa fa-retweet" ></i>Reset</button>


                    </div>

                    </form>

The script

<script type="text/javascript">
               $(document).ready(function(){
                   $("#branch_code").change(function(){
                     var branch =$("#branch_code").val();
                     $.ajax({
                    type:"post",
                    url:"auto_branch_customer.php",
                    data:"branch_code="+branch,
                    success:function(data){
                          $("#w_date").html(data);
                    }
                     });
                   });
               });
        </script>

The Php

    <?php
$branchcode = $_POST['branch_code'];
$sql = "SELECT working_date FROM days WHERE branch_code = $branchcode";
$result = mysql_query($sql);

while($row = mysql_fetch_array($result)) {
echo "{$row['working_date']}";
}
?>