You receive an inheritance of $100,000. However the terms of the bequest specify that you cannot take possession of the cash until the sum has grown to $250,000. The money is being held in trust for you in an account that is currently paying 10%, compounded quarterly. The bank where the account is held guarantees the rate is fixed for the first five years, but thereafter may increase, but will not decrease. If the interest rate increases, the increase will not be more than 200 basis points (2%) above the current rate (total, ever).

What is

a) the soonest, and

b) the latest you will be able to claim your inheritance?