Question

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 = 15n + 143, where an is the value of the stock and n is the number of years.


Year Price
1 $158.00
2 $173.00
3 $188.00
4 $203.00
5 $218.00


Stock B: Equation: an = 24(1.1)n − 1, where an is the value of the stock and n is the number of years.

Year Price
1 $24.00
2 $26.40
3 $29.04
4 $31.94
5 $35.14


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?

HELPPPPPP 100 POINTS PLEASE

Answer 1

Find 50th term on both

#1

• 15(50)+143
• 893

#2

• 24(1.1)^{50-1}
• 24(1.1)⁴⁹
• 2561.25

Difference

• 2561.25-893
• $1668.25

Answer 2

Use the formulas and find 5th term of both and compare

Stock A

• a₅₀ = 15(50) + 143 = $893

Stock B

• a₅₀ = 24(1.1)⁴⁹ = $2561.25

As we see Stock B share has greater value in 50 years and the difference is:

• $2561.25 - $893 = $1668.25