Basically well formate for carbon date is YYYY-MM-DD .
$nowMonth = date('F');
$getInterval = 'get interval value from database';
if($getInterval == 1){
$doDate = Carbon::now()->addMonths(1);
//do whatever you want
}
if($getInterval == 3){
$firstJanuary = new \DateTime('first day of January 2016');
$firstApril = new \DateTime('first day of April 2016');
......
//do whatever you want
}
```
Hope will work for you...