Which option has the greatest value in a comparison of: $1,000,000; the value of 1 cent doubled daily for 30 days; 10 shares of Berkshire Hathaway stock; or $500,000?

Which option has the greatest value in a comparison of: $1,000,000; the value of 1 cent doubled daily for 30 days; 10 shares of Berkshire Hathaway stock; or $500,000?

• A. $1,000,000
• B. $500,000
• C. 10 shares of Berkshire Hathaway stock
• D. The value of 1 cent doubled daily for 30 days

Answer: (D)

The key idea is exponential growth from compounding. A tiny amount that doubles every day can become very large very quickly. Starting with 1 cent, after 30 days you have 0.01 × 2^30 dollars. Since 2^30 is 1,073,741,824, that total is 0.01 × 1,073,741,824 = 10,737,418.24 dollars. That’s about $10.7 million, which easily surpasses the fixed sums of $1,000,000 and $500,000. Ten shares of Berkshire Hathaway depend on the stock price, which can fluctuate. Even if each share is hundreds of thousands of dollars, ten shares would typically amount to a few million at most, which is still less than the $10.7 million from the doubling penny. Because the doubling scenario yields a fixed, clearly larger value under these conditions, it is the greatest option.

The key idea is exponential growth from compounding. A tiny amount that doubles every day can become very large very quickly.

Starting with 1 cent, after 30 days you have 0.01 × 2^30 dollars. Since 2^30 is 1,073,741,824, that total is 0.01 × 1,073,741,824 = 10,737,418.24 dollars. That’s about $10.7 million, which easily surpasses the fixed sums of $1,000,000 and $500,000.

Ten shares of Berkshire Hathaway depend on the stock price, which can fluctuate. Even if each share is hundreds of thousands of dollars, ten shares would typically amount to a few million at most, which is still less than the $10.7 million from the doubling penny. Because the doubling scenario yields a fixed, clearly larger value under these conditions, it is the greatest option.