Insert multiple rows avoiding cursors and loops in SQL Server

I'm trying to insert multiple rows that correspond to each payment that several clients have to do in a given date.
Obviously there are 2 tables, the first being the clients table:

cust_id, name ...
1, John Doe
2, Jane Smith
...

And the second being the payments table, using a serialized payment_id and incremental dates by 1 month for each payment: (ID is an identity column)

ID, cust_id, payment_id, due_date
1, 1, 1, 2016-01-01
2, 1, 2, 2016-02-01
3, 1, 3, 2016-03-01
5, 2, 1, 2016-01-01
6, 2, 2, 2016-02-01
7, 2, 3, 2016-03-01
...

I've seen that using WHILE loops should be avoided as stated in this answer, and cursors would take a long time if we are speaking of thousands of clients and tens of payments for each one.

Any pointer would help, thanks.

-- Edited to correct a typo in the title.