There is legend of a king who wanted to reward a boy for a good deed. The king gave the boy a choice. He could have $1,000,000 at once, or he could be rewarded daily for a 30-day month, with one penny on the first day, two pennies on the second day, and so on, receiving twice as many pennies each day as the previous day. How much would the second option be worth?

Question

Mathematics

Amelia Herman

5 April, 07:31

There is legend of a king who wanted to reward a boy for a good deed. The king gave the boy a choice. He could have $1,000,000 at once, or he could be rewarded daily for a 30-day month, with one penny on the first day, two pennies on the second day, and so on, receiving twice as many pennies each day as the previous day. How much would the second option be worth?

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Answers (1)

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Melanie May · Answer 1

10,737,418.23 dollars

Step-by-step explanation:

The second option would be worth 2^x - 1, where x = days passed.

Because there are 30 days, the answer is 2^30 - 1.

2^30 = 1073741824, making 2^30 - 1 = 1073741823.

It would be worth = 1073741823 cents, making it = 10,737,418.23 dollars