Someone has offered to buy you a financial instrument that has the following cash flows:

-  You will not receive any cash for the first five years.  The first time you will receive a cash flow will be at the end of year 6.  You will receive $100 at the end of year 6, $200 at the end of  year 8, and $300 at the end of year 10.

-  You will receive another payment of $100 at the end of year 11, and the payment will grow at a rate of 6% forever.

-  You will need to pay a service fee.  The service fee is as follows:  you will pay $100 each year from year 1 to year 5 (i.e. you will make 5 payments in total.  The first payment will occur at the end of year 1, and the last payment will occur at the end of year 5)

Suppose that the discount rate is 10%.  How much this financial instrument is worth to you?

***  You have to show your work to get credit.

 

2) 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?  Points: 6

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?