An account credits interest at an effective annual rate of 2% for the first 10 years and according to a force of interest ()=2/(1+^2)thereafter.

a) Deposits are made continuously into the account at a rate 1()=1. Find the accumulated value after 15 years.

b) Deposits in the account stop after fifteen years. The accumulated amount (found above) is used to fund a continuous withdrawal at a rate 2()=2. Can this withdrawal scheme be carried forever? Justify your answer.