Jim works full time and has a good job that generates a stable income. Jim currently has $200,000 cash in his savings account for retirement. To maximise his savings for retirement, Jim plans to deposit $1,000 every month into this saving account from now onwards. The savings account earns an after-tax interest rate of 1.25% p.a., compounding monthly. Jim is highly committed to this monthly contribution to the savings account and will not withdraw any funds from this account. Jim plans to retire in 20 years.

a) How much will Jim have in this savings account when he retires 20 years later? Show all work clearly.

b) Suppose that at the time Jim retires he has a total cash from all his assets (including the above savings) in the amount of $1,000,000. It is estimated that this fund will be earning an interest rate of 3% p.a., with interests to be compounded monthly. Jim believes that he can live healthily for 35 years after he retires and he intends to spend this savings by withdrawing an equal amount of money every month from this fund for 35 years. What is the equal amount of money that he withdraw from this savings account every month for 35 years? (Assuming there will be no more cash to be deposited into this account over the 35 years.)

Show all the workings. No Excel.