George contemplates the purchase of 100 shares of a stock...

George contemplates the purchase of 100 shares of a stock selling for $\$ 15$ per share. The stock pays no dividends. The history of the stock indicates that it should grow at an annual rate of $15 \%$ per year. How much should the 100 shares of stock be worth in 5 years?

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Key Concepts

Compound Interest

Compound interest is the process by which an investment grows exponentially because interest is earned on both the initial principal and the accumulated interest from previous periods. This recurring application results in the value increasing at a rate that combines both the initial amount and the interest earned over time.

Future Value Calculation

Future value refers to the value of an asset or investment at a specific future date, calculated using a growth rate over time. The calculation typically involves multiplying the initial amount by a growth factor raised to the number of periods, reflecting how investments appreciate due to compounding.

Exponential Growth

Exponential growth describes a process where the rate of increase is proportional to the current value, leading to growth that accelerates over time. This concept is fundamental in situations where each period's increase builds on the previous period's accumulation, a common characteristic of compound interest.

Time Value of Money

The time value of money is a core principle in finance that underscores the idea that a sum of money has greater potential value now than the same sum in the future. This is due to its capacity to earn interest or returns over time, making future cash flows less valuable than immediate ones when adjusted for potential growth.

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