That sounds good, here's a quick design for you (based on your current data):
Code:
tblPeople
  PersonID (unique ref)
  LastName
  Firstname

tblPayment
  PersonID (link to tblPeople)
  LastPayDate
  BalanceDue 
  AmountPaid
I think the tblPayment table needs a redesign, but how depends on exactly how it should work. Possibly this:
Code:
tblPaymentsMade
  PersonID (link to tblPeople)
  PayDate  (you can calculate a "last paid" date from this)
  AmountPaid

tblAmountOwed
  PersonID (link to tblPeople)
  DateOwed
  BalanceDue