The value of a stock share in a new technology company has been increasing at a rate of 8.6% quarterly. The initial price of one share was $102.15. An investor plans to sell once the value of one share reaches $233.10. If t is the number of quarters since the initial price of one share was set, which equation could be used to determine how long it will take the share to reach $233.10, assuming it continues to grow at the same rate?

Question

Mathematics

Margaret Roberson

3 August, 12:02

The value of a stock share in a new technology company has been increasing at a rate of 8.6% quarterly. The initial price of one share was $102.15. An investor plans to sell once the value of one share reaches $233.10. If t is the number of quarters since the initial price of one share was set, which equation could be used to determine how long it will take the share to reach $233.10, assuming it continues to grow at the same rate?

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Johnny Andersen · Answer 1

Answer: 39 quarter

The value of a stock share in a new technology company has been increasing at a rate of 8.6% quarterly. That means the stock will increase by 8.6%/4 = 2.15% rate per quarter. The exponent function to find the number of money the investor have would be:

an = $102.15 (1.0215) ^t

The time needed for getting $233.10 would be:

an = $102.15 (1.0215) ^t

$233.10 = $102.15 (1.0215) ^t

2.2819 * $102.15 = $102.15 (1.0215) ^t

2.2819 = (1.0215) ^t

t = log1.0215 2.2819

t = 39