Suppose a customer has deposited $2,000,000. In three years their deposit had grown to $2,300,000 and two years after that it had grown to $2,600,000. Assume that the force of interest varied linearly according to (t) = at + b during this time.

(a) Find the force of interest after exactly four years after the initial deposit was made.

(b) Find the accumulated amount of money after exactly four years after the initial deposit was made.