At some point, you may have seen the question, “Would you rather have a penny that doubles each day for a month or 1 million dollars?” You may be wondering whether the option you’d instinctively choose is the best option. Fortunately, you can figure it out with a little math. If you had to pick between a penny that doubles each day for a month or 1 million dollars, here’s what you need to know.
A Penny That Doubles Each Day for a Month or 1 Million Dollars
The challenging question about which option you’d take is actually based on an Indian fable. The “One Grain of Rice” fable – as it’s generally referred to – involves a raja who was keeping rice from his people. A village girl saw rice falling that was supposed to head to the raja, and, in return for her good deed of collecting it and giving it to the raja, she was offered a reward.
The girl initially asked for one grain of rice. When the raja scoffed, she altered her request to one grain of rice that doubles each day for thirty days. The raja accepted, only to discover that the end sum was quite sizeable.
In many cases, a person’s first instinct when asked to choose between a penny that doubles each day for a month or 1 million dollars is to take the million. Mainly, it’s because $1,000,000 and $0.01 are so vastly different, making it appear like the penny option couldn’t catch up.
However, by going with the penny instead, you actually come out dramatically ahead. Here’s the full breakdown by day:
Day 1 – 10
1$0.012$0.023$0.044$0.085$0.166$0.327$0.648$1.289$2.5610$5.12
Day 11 – 20
11$10.2412$20.4813$40.9614$81.9215$163.8416$327.6817$655.3618$1,310.7219$2,621.4420$5,242.88
Day 21 – 30
21$10,485.7622$20,971.5223$41,943.0424$83,886.0825$167,772.1626$335,544.3227$671,088.6428$1,342,177.2829$2,684,354.5630$5,368,709.12
Ultimately, choosing the penny leads to more than five times the million-dollar alternative. Many consider this a lesson of the power of investing and long-term monetary growth, showing just what could happen if you make sure that your money is working for you.
If you had to choose a penny that doubles each day for a month or 1 million dollars before reading the article above, what would you have chosen? Are you surprised that the penny puts you ahead, or did you already know that was the case? Share your thoughts in the comments below.
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Tamila McDonald is a U.S. Army veteran with 20 years of service, including five years as a military financial advisor. After retiring from the Army, she spent eight years as an AFCPE-certified personal financial advisor for wounded warriors and their families. Now she writes about personal finance and benefits programs for numerous financial websites.
