Final answer:
The question discusses how $1 changes with investing over multiple periods given three scenarios of IRR. Negative IRR means the investment loses value, while positive IRR leads to growth through compound interest. One must note that IRR lower than -100% is not realistic as it means losing more than the total investment.
Step-by-step explanation:
The student's question is about understanding what happens to $1 after multiple periods of investing, considering different Internal Rate of Return (IRR) scenarios. The IRR is a measure of an investment's rate of return, and these scenarios include IRR that is less than -100%, between -100% and 0%, and between 0% and 100%. Using the power of compound interest, we can determine how an investment grows over time.
Scenarios:
If IRR < -100%, the scenario is generally not realistic as it suggests that you would lose more than the entire investment, which is not possible.
For IRR > -100% and < 0%, each period you would lose some value, getting closer to zero, but never quite reaching it.
With an IRR > 0% and < 100%, the $1 investment would grow at a rate according to the specific positive IRR.
Utilizing the principle of compound interest, investments can increase in value over time if the IRR is positive. For example, an investment using a 7% real annual rate of return will increase nearly fifteen-fold over 40 years. This illustrates the benefits of saving early and allowing returns to compound.