Retrieving monthly rainfall averages for Feature Collection in Google Earth Engine?

I am trying to retrieve monthly rainfall averages for points stored in a feature collection. I have checked other posts with similar questions but I cannot seem to figure out how to adapt their solutions to my case. This is my code for the daily precipitation values.

How would I have to modify it to get monthly values?

var fg_points = 
ee.FeatureCollection('ft:17ZWOtlTiq6ehKrp8KhmDhsxwP0lVKHaGYaJqo_Uj');

//generate point and dates
var start = ee.Date('1994-01-01');
var finish = ee.Date('2017-01-01');
var daily = ee.ImageCollection('UCSB-CHG/CHIRPS/DAILY')
.filterDate(start, finish);


var mapfunc = function(feat) {
  var geom = feat.geometry()
  var addProp = function(img, f) {

    var newf = ee.Feature(f)
    var date = img.date().format("MM_dd_YYYY")
    var value = img.reduceRegion(ee.Reducer.first(), geom, 
    30).get('precipitation')
    return ee.Feature(ee.Algorithms.If(value,
                                   newf.set(date, ee.String(value)),
                                   newf.set(date, ee.String('No data'))))
  }
  var newfeat = ee.Feature(daily.iterate(addProp, feat))
  return newfeat

 };

 var newft = fg_points.map(mapfunc);


Export.table.toDrive(newft,
"PrecipitationHTL",
"PrecipitationHTL",
"PrecipitationHTL");