To Sum Cells Until Preset Value Is Reached

I have a spreadsheet with time values incremented in column A.

In column K, there are numerical values that correspond to the time in column A.

Elsewhere, a specific time is chosen from which to begin the summing of the values in column K.

I need to be able to sum the values in column K until preset values are reached. Then I need to know at which corresponding time value the summing loop stops.

For example, a time of 11:00 AM is chosen as the "start time". I want to sum the values in column K until they are >= 2.000.

At that point, I need to know what the cell value was in colum A that is in the same row as the last cell value in column K.

I can't seem to do it with simple Excel functions without falling into a self referencing loop. So what I need is for a VBA loop to lookup the appropriate values in column K, sum the values, check the total, and continue the loop until the preset total is reached. Then look up the value in column A in the last row of summed values, and return that value.