Final answer:
Carol seeks to retire with $500,000 by investing in an ordinary annuity; compound interest plays a significant role in the growth of such investments. Comparing a $3,000 investment at 7% annual return over 40 years to Carol's scenario highlights the importance of rate of return and investment period. Fees should also be considered as they can affect the final amount of savings.
Step-by-step explanation:
Carol wishes to retire with $500,000 in 25 years by investing in an ordinary annuity offered by her credit union. To understand how much she needs to save, we can use the concept of compound interest, which is the interest on both the initial principal and the accumulated interest from previous periods. A good example to illustrate compound growth is by considering a $3,000 investment at a 7% annual rate of return, which after 40 years, will grow to $44,923 as shown by the equation 3,000(1+.07)40 = $44,923.
However, considering the retirement goal and the period of 25 years, Carol would need to calculate the specific annuity payment, adjusting for expected rate of return and the timeframe, to ensure her annuity results in the desired retirement sum. Additionally, fees like the administrative fees charged on retirement funds, which can be as much as 0.25%, must be considered as this impacts the effective rate of return. For instance, if Alexx and Spenser each invest $5,000 but Alexx earns a rate of return of 5% while Spenser's net return after fees is 4.75%, after 30 years, Alexx would have more due to the difference in rates compounded over time.