Final answer:
The questions involve calculating the future value of a retirement investment for Charles and comparing investment outcomes for Alexx and Spenser. To determine Rosalie's lump sum buying power, we'd discount its future value by the inflation rate over 16 years. For Alexx and Spenser, we'd calculate the future value of investments with two different rates over 30 years to see the difference.
Step-by-step explanation:
The student is asking about the future value of Charles's investments assuming a 6% annual return over 20 years. However, the provided information references a different scenario involving Rosalie the Retiree and her retirement lump sum being affected by inflation. To calculate Rosalie's situation, we need to adjust the future value of the lump sum by the inflation rate to determine its buying power in today's dollars. For Alexx and Spenser's scenario, we'd use the formula for the future value of an investment adjusting for different annual returns over 30 years to determine the difference in their investment outcomes.
For Rosalie's scenario and assuming a constant inflation rate, we use the present value formula to discount the future value of the $20,000 payment. Using the formula PV = FV / (1 + r)^n, where PV is present value, FV is future value, r is the inflation rate (6% or 0.06), and n is the number of years (16), we can calculate the buying power of the $20,000 in today's dollars.
For Alexx and Spenser, we'd apply the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (5% for Alexx, reduced by 0.25% for Spenser), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years (30 years in this case).