how to add days to java simple date format

Basically, you can simple use a Calendar which has the capacity to automatically roll the various fields of a date based on the changes to a single field, for example...

Calendar cal = Calendar.getInstance();
cal.setTime(date);
cal.add(Calendar.DATE, 120);
date = cal.getTime();

Take a closer look at Calendar for more details.

Yes, there is a way to do this using Joda Time, but I could type this example quicker ;)

Update with JodaTime example

The following is an example using JodaTime. You could parse the String value directly using JodaTime, but since you've already done that, I've not bothered...

Date date = ...;
DateTime dt = new DateTime(date);
dt = dt.plusDays(120);
date = dt.toDate();

I would suggest you use Joda DateTime if possible. The advantage is it handles TimeZone very gracefully. Here's how to add days:

DateTime added = dt.plusDays(120);

Reference: http://joda-time.sourceforge.net/apidocs/org/joda/time/DateTime.html#plusDays(int)