Limit Output of Array Formulas to 128 Characters in Google Sheets

If you add the following formula in cell D2:

=ARRAYFORMULA(FILTER(C2:C;C2:C<>"")*1.2)

then it will take on the complete column, via the array. The FILTER function, is to make sure no empty cells are taken into account.

I've added the result into the file you shared with us.

If you did not insist on array-based formula, then

sumifs(C:C, A:A, A2, B:B, "<="&B2)

entered in D2 and copied around the D column, would do the job.

I don't think that an arrayformula-based solution exists, because arrayformula runs through an array once, performing some element-wise operations. You want to compare each element with all others, which is one step further in complexity (a double for loop).

But you can use a custom function, something like =runningtotal(A2:A, B2:B, C2:C) which processes the columns and returns an array of running totals. The script implementing this function is below; add it via Tools > Script Editor. The logic is quite straightforward: as said above, it's a double for loop.

function runningTotal(names, dates, amounts) {
  var sum, totals = [], n = names.length;
  if (dates.length != n || amounts.length != n) {
    return 'Error: need three columns of equal length'; 
  }
  for (var i = 0; i < n; i++) {
    if (names[i][0]) {
      sum = 0;
      for (var j = 0; j < n; j++) {
        if (names[j][0] == names[i][0] && dates[j][0] <= dates[i][0]) {
          sum = sum + amounts[j][0];
        }
      }
    }
    else {
      sum = '';
    }
    totals.push([sum]);
  }
  return totals;
}