You have just joined a regional investment banking firm. They have 
            offered you two different salary arrangements. You can have $81,000 
            per year for the next 3 years or $60,000 per year for the next 3 
            years, along with a $50,000 signing bonus today. If the market 
            interest rate is 16%, what is the present value of the best salary 
            arrangement?

Hello fatima!
You can find a good discussion on the subject of present value at:

Calculating the Present and Future Value of Annuities
http://www.investopedia.com/articles/03/101503.asp

In the case you give, the present value (PV) of the $81,000 per year
option would be (assuming that the first payment comes one year from
now):

PV = 81000/(1+0.16)^1  +  81000/1.16^2  + 81000/1.16^3
   = 69827.58          +   60196.19     +   51893.27
   = 181917.04

So the present value of this option is $181,917.04

The present value of $60,000 per year plus bonus option would be
(again, assuming that the first $60,000 payment comes one year from
now):

PV = 50000 + 60000/1.16^1 + 60000/1.16^2 + 60000/1.16^3
   = 184753.37

So the present value of this option is $184,753.37. Since it's higher
than the other one, this is the best salary arrangement for you.


I hope this helps!
Best wishes,
elmarto