My answer takes into account that you don't want to reformat your data into a traditional data warehouse schema. If it gets you further down the road then good for you but I suspect you'll run into more of these problems as you grow your project. It might be worth tinkering with how you might transform the data into a star schema before you need it.
I can suggest a few options. The first that comes to mind is to make a degenerate dimension in the accounts cube that is based on the payments fact table. The following example answers your "all accounts that have a payment" problem but this should work for similar questions. I assumed an account statement date as the last day of each calendar month so you'll want to count payments made in each calendar month.
create table accounts_fact
( account_id int not null,
statement_date datetime not null,
bal int not null,
constraint acc_pk primary key (account_id, statement_date)
)
create table payments_fact
( account_id int not null,
payment_date datetime not null,
amount money not null
)
insert into accounts_fact values (1, '20100131', 100)
insert into accounts_fact values (1, '20100228', 120)
insert into accounts_fact values (1, '20100331', 0)
insert into accounts_fact values (2, '20100131', 100)
insert into accounts_fact values (2, '20100228', 20)
insert into accounts_fact values (2, '20100331', 50)
insert into accounts_fact values (3, '20100131', 10)
insert into accounts_fact values (3, '20100228', 30)
insert into accounts_fact values (3, '20100331', 50)
insert into payments_fact values (1, '20100112', 50)
insert into payments_fact values (1, '20100118', 60)
insert into payments_fact values (1, '20100215', 70)
insert into payments_fact values (1, '20100318', 80)
insert into payments_fact values (1, '20100331', 90)
insert into payments_fact values (2, '20100112', 50)
insert into payments_fact values (2, '20100215', 60)
insert into payments_fact values (2, '20100320', 70)
insert into payments_fact values (3, '20100101', 50)
insert into payments_fact values (3, '20100118', 60)
insert into payments_fact values (3, '20100318', 70)
create view dim_AccountPayments
as
select acc.account_id, acc.statement_date,
sum(case when pay.payment_date IS NULL THEN 0
else 1
end) as payment_count
from accounts_fact acc
left outer join payments_fact pay on acc.account_id = pay.account_id
and pay.payment_date >= dateadd(mm, -1, dateadd(dd, 1, acc.statement_date))
and pay.payment_date <= acc.statement_date
group by acc.account_id, acc.statement_date
select * from dim_AccountPayments
This produces the following results:
account_id statement_date payment_count
1 2010-01-31 00:00:00.000 2
1 2010-02-28 00:00:00.000 1
1 2010-03-31 00:00:00.000 2
2 2010-01-31 00:00:00.000 1
2 2010-02-28 00:00:00.000 1
2 2010-03-31 00:00:00.000 1
3 2010-01-31 00:00:00.000 2
3 2010-02-28 00:00:00.000 0
3 2010-03-31 00:00:00.000 1
It should now be a doddle to make a payments count dimension in your accounts cube. For extra points, remove the group by and sum in the view to let SSAS do the aggregation; it suited me to show the results table above. Use the view's SQL in your data source view you don't have create view permission in the source database.
Option 2 would be to make payment count from the view above a measure in the accounts cube. You can do this similarly to the above solution except make your accounts fact use a view similar to dim_AccountPayments. This time you must group by all key fields and aggregate the measures in the database... Very ugly. I don't recommend it but it is possible.
If you go with option 1 then it's simple enough to make a named set in the account payments dimension called 'Made a payment this month' which is children of all filtered to remove 0.
I hope I understood your question. I did have to make quite a few assumptions about your data structures but I hope it's useful.
Good luck.