Final answer:
Yes, it is true that if you start with a penny and double it every day, after 30 days you would have over a million dollars. This concept is related to exponential growth, similar to the effects of compound interest over time.
Step-by-step explanation:
If you start with a penny and double the amount each day, by the end of 30 days you would indeed have a substantial amount of money, but the question is whether it would be over a million dollars. Each day, you multiply the previous day's total by two, which is an example of exponential growth. Let's examine this mathematically:
To calculate the amount on day 30, you would use the formula for exponential growth: Penny Amount * (2^(Number of Days - 1)). For day 30, this would be $0.01 * (2^(30 - 1)), which equals to $10,737,418.24. Therefore, it is true that you would have over a million dollars after 30 days.
The power of compound interest is similar to this concept, where money grows over time at a specified interest rate. Starting to save money early in life and letting it grow through compound interest can significantly increase the total sum, as indicated by the illustrative example of starting with a $3,000 investment at a 7% real annual rate of return, which grows to $44,923 after 40 years.