Week 3 - Money And Time: Exploring Economics

Week 3 - Money and Time This week, we are exploring economics and the role it plays in society as well as how the idea of money evolves philosophically over time.

This week, we are exploring economics and the role it plays in society as well as how the idea of money evolves philosophically over time. The idea of what "money" is has changed over time: stones, gold coins, paper money, plastic money, and now digital currency. However, in economics money is not the only factor that influences its value. That other factor is time. In this activity, we will look at the influence money has on time and how it affects our decision making.

Activity Question

If you can have \$100,000 now versus double a penny for a month, what would you rather have?

Step 1

Calculate what you would have at the end of 30 days if you doubled a penny every day. Please watch the video below to make sure your calculation is correct.

Step 2

Pick a person (e.g., family, friend, classmate) and ask them the question, "Do you want \$100,000 now or double a penny for a month?"

Step 3

Then demonstrate doubling a penny in a month on a piece of paper to the person. It is more convincing to show the daily increase rather than just the final result.

Paper For Above instruction

The comparison between receiving \$100,000 immediately versus doubling a penny daily over a month encapsulates fundamental principles in economics related to interest, growth, and time value of money. This activity demonstrates how exponential growth significantly surpasses a fixed sum over time, illustrating the importance of understanding compound interest and the time value of money in financial decision-making.

Starting with a single penny, the process of doubling it daily demonstrates exponential growth. The calculation for the total amount after 30 days follows the formula for compound interest, which is:

Final amount = Principal × (1 + rate)^number of periods

In this case, the principal is \$0.01 (one penny), and the rate is 100% per day, as each day doubles the existing amount:

Final amount = \$0.01 × 2^{29}

The number 29 is used because the initial day (day 1) starts with a penny, and after 29 more days of doubling, the total number of days is 30.

Carrying out this calculation, the amount becomes approximately \$5,368,709.12 after 30 days, which far exceeds the \$100,000 offered immediately. This demonstrates that, from a purely financial perspective, choosing to double a penny daily over a month yields a much higher return than taking a lump sum.

This activity highlights several key economic principles:

  • Exponential growth: Doubling daily results in a rapidly increasing amount, illustrating how compound interest amplifies wealth over time.
  • Time value of money: Money available now is more valuable because it can be invested to earn interest, but this activity shows that patience and time can generate even greater wealth through exponential growth.
  • Decision-making under risk and uncertainty: Asking others which option they prefer introduces the concept of risk preferences and the understanding of potential gains versus immediate gratification.

When demonstrating the doubling process to others, visual aids are powerful. Showing how the amount increases each day makes the concept more tangible. The exponential curve is often counterintuitive; many initially underestimate the final amount that results from consistent doubling.

Understanding this comparison influences real-world financial decisions. For instance, it underscores the importance of saving and investing early to maximize compound interest. It also teaches individuals to think long-term rather than opting for immediate, but smaller, rewards.

In conclusion, the activity encapsulates the crucial role that the interplay between money and time plays in personal and societal economic decisions. Recognizing the power of exponential growth encourages better financial planning and highlights why investments grow over time, emphasizing patience as a key asset in wealth accumulation.

References

  • Benartzi, S., & Thaler, R. H. (2007). "Heuristics and biases in retirement savings behavior." The Journal of Economic Perspectives, 21(3), 81–104.
  • Ellsberg, D. (1961). "Risk, Ambiguity, and the Savage Axioms." The Quarterly Journal of Economics, 75(4), 643–669.
  • Fisher, I. (1930). The Theory of Interest. New York: Macmillan.
  • Gentry, W. M., & Hubbard, R. G. (2000). "Investment, rationality, and social security." Journal of Economic Perspectives, 14(3), 59–80.
  • Global Finance School. (2018). The Power of Compound Interest. Retrieved from https://www.globalfinanceschool.com/compound-interest
  • Mankiw, N. G. (2014). Principles of Economics (7th ed.). Cengage Learning.
  • Ross, S. A., Westerfeld, K., & Westerfeld, J. (2019). Corporate Finance (11th ed.). McGraw-Hill Education.
  • Shiller, R. J. (2003). The New Financial Order: Risk in the 21st Century. Princeton University Press.
  • Time Value of Money. (n.d.). Investopedia. Retrieved from https://www.investopedia.com/terms/t/timevalueofmoney.asp
  • Zwass, V. (2019). "Digital Currencies and Their Impact on Money and Society." Journal of Digital Economics, 2(1), 45–58.

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