Final answer:
To fund a retirement goal of $1 million with a lump sum deposit today, if you plan to retire later rather than sooner and earn a high rate of interest, you can deposit a smaller amount due to the effects of compound interest, which allows for greater growth over a longer period.
Step-by-step explanation:
The goal is to have $1 million in your retirement savings on the day you retire. To fund this goal, you will make one lump sum deposit today. The correct choice that would allow you to deposit a smaller lump sum today is C - later; sooner; high. The logic behind this option is that the longer you have until retirement, the more time compound interest can work in your favor. Moreover, a higher interest rate will accelerate the growth of your savings over time.
Let's consider an example: If the rate of return is 7% annually (compound interest), a $3,000 investment will have multiplied nearly fifteen fold after 40 years (using the formula for compound interest, $3,000(1+0.07)40 = $44,923). Therefore, if you plan to retire later rather than sooner and earn a high rate of interest, you can indeed allow compound interest to significantly increase your savings over time, requiring a smaller initial investment. Conversely, if you plan to retire sooner, you would need a larger lump sum today to meet your $1 million target because there's less time for compound interest to accumulate.
Remember, starting early with your savings and letting them grow through compound interest makes it more attainable to reach your retirement goals, as shown by the example of saving and investing $3,000 once.