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A stock market analyst observes the following for the price of two stocks that he owns, one of which is increasing at an exponential rate (geometric) and the other is increasing in a linear fashion (arithmetic).
Stock A: Equation: an = 10n + 152, where an is the value of the stock and n is the number of years.
YearPrice
1$162.00
2$172.00
3$182.00
4$192.00
5$202.00
Stock B: Equation: an = 35(1.10)n − 1, where an is the value of the stock and n is the number of years.
YearPrice
1$35.00
2$38.50
3$42.35
4$46.59
5$51.24
Assuming these stock values continue to increase in the same manner until retirement, which stock option is worth more in 50 years and how much more is this stock worth per share?
A Stock A is worth more in 50 years; $3,456.70 more per share
B Stock B is worth more in 50 years; $652.00 more per share
C StockA is worth more in 50 years; $2,905.46 more per share
D Stock B is worth more in 50 years; $3,083.16 more per share
First of all, your second equation is the exponential one but is written incorrectly. It should look like this:
an = 35(1.10)^(n − 1). So, in 50 years you will have:
a(50) = 35(1.10)^(50 - 1)
a(50) = 35(1.10)^49
a(50) = 35 x 106.7189571......
a(50) = $3,735.16 - The value of stock B in 50 years.
an = 10n + 152
a(50) =10 x 50 + 152
a(50) =500 + 152
a(50) =$652 - This is the value of stock A in 50 years
Stock B - stock A =$3,735.16 - $652 =$3,083.16 - This is how much more will stock B worth than stock A in 50 years. Or, "D" on your list of multiple choices.
