How does the time value of money affect the retirement savings of two individuals who received $10,000 gifts but invested them differently, according to the chapter's example?

The time value of money significantly impacts the retirement savings of two individuals who each received $10,000 gifts but invested them differently. One person invested the entire amount immediately and earned 10 percent annually for 46 years, resulting in over $800,000 at retirement. In contrast, the other person delayed investing for 15 years, resulting in only about $192,000 after investing for 31 years, demonstrating the importance of early investment and compounding interest.

The example illustrates that the individual who invested the $10,000 immediately benefited from 46 years of compounding at a 10 percent annual interest rate, leading to substantial growth of their investment. Conversely, the individual who carried the cash for 15 years before investing missed out on 15 years of potential earnings, resulting in a significantly lower retirement savings of approximately $192,000 after only 31 years of investment. This stark difference of over $600,000 underscores the critical role of the time value of money in retirement planning.