Jim is now 40, and he wishes to retire when he is 60 years old. He wants to have $1 million cash when he retires. He just received $100,000 from inheritance, and will invest that today.  

Assume that the annual interest rate is 10%, and interest is compounded annually unless specified otherwise:

 

a. Jim knows that he will not be able to have $1 million unless he makes additional investment.  So, he decides the following: he will invest $10,000 every year for 10 years.He will start investing 1 year from today (i.e. when he is 41), and he will make his last investment when he is 50.  

The accumulated fund will be left invested until he retires. Will this additional investment fulfill his retirement goal of having $1 million when he retires?  

 

b.  Now suppose that Jim is 50.  He has changed his retirement goal. He wants to make sure of just one thing he wants to withdraw $50,000 per year for 30 years after he retires (i.e. the first withdrawal will begin when he is 60)? How much money must he have saved up when he retires to support the new retirement goal?