How to calculate running total based on dynamic values?

Question

I need to calculate the running total in which the target column is changing along with the time. Its something which aws does. Charging based for only what you use. So how do I aggregate sum of payments and charges.

Currently I'm storing the running total in the balance column and that sum is calculated using sum of charges - sum of payments.

Here's what the table looks like

      Invoices
id    tx_type    amount   live 
 1     Charge     100      true             // live = true means that the amount will be updated and the meter is ticking
 2     Payment    100      false
 3     Charge     50       true
 4     Charge     75       false
 5     Payment    125      false

UserBalances

id  user_id   balance
1     1         0.0

So the balance at this instant will be 0 but after couple of seconds should be different as meter is still ticking. How do I get the sum of amount field which is ever changing?

PS: I'm using ruby on rails and postgresql

Thanks