Answer
See sample answer below.
Work Step by Step
The banker is either lying or he doesn't know how continuous compounding works (which is doubtful since he is a banker).
The idea behind continuous compounding is that your balance is updated every second, 10th of a second, millionth of a second, etc. But in reality, all the bank needs is a formula for continuous compounding to calculate the balance at a given time.
So, the balance is calculated when you need the information, once in a while, not every billionth of a second.
