Jag tror att detta ger dig vad du letar efter (ett av många sätt):
SELECT t.diapason, COUNT(*) AS 'number_of_users'
FROM (SELECT CASE
when amount<100 then '0-100'
when amount>=100 then '100 +' END AS diapason
FROM
(SELECT SUM(amount) AS amount
FROM payments
INNER JOIN (SELECT DISTINCT user_id FROM activity where login_time between '2012-04-05' and '2012-04-12') AS a ON payments.user_id = a.user_id
GROUP BY payments.user_id) AS P
) t
GROUP BY t.diapason
ORDER BY number_of_users desc
;