Note: A 3% increase in the price means you mulitply by 103%, or by 1.03.

This is essentially a geometric series. Let t be the number of years and P the price of the shoes in dollars. Then:

So, we want to know t when P = $100.

Now take the logarithm of both sides. I personally prefer log base e = "ln", but pick which ever base you prefer. The choice does not matter.

So t = 5.5 years or so.

-Dan