A stock market analyst observes the following for the price of two stocks that he owns, one of which is growing in a linear fashion (arithmetic) and the other of which is growing at an exponential rate (geometric).
Stock A: Equation: an = 25n + 60, where an is the value of the stock and n is the number of years
Stock B: Equation: an = 12(1.11)n − 1, where an is the value of the stock and n is the number of years
Assuming these stock values continue to grow in the same manner until retirement, which stock option will be worth more in 42 years, and how much more (rounded to the nearest cent) will this stock be worth per share? Stock A; $244.19 Stock B; $865.81 Stock A; $1,110.00 Stock B; $221.18
What don't you understand about the question? You have ALL the information you need to answer the question very easily. The only small mistake you have is the equation of stock B. It should be written like this:
a(n) =12*(1.11)^(n - 1).
All you have to do is to substitute 42 years for n in both equations as follows:
Stock A: a(n) =25n + 60 =(25*42) + 60 =$1,110 - value of stock A after 42 years.
Stock B: a(n) =12*(1.11)^(n - 1) =12*(1.11)^(42 - 1) =$865.81 - value of stock B after 42 years.
$1,110 - $865.81 =$244.19 - this is the difference in value between stock A and stock B after 42 years.