Final answer:
To find out how much Carson will have saved by the end of year 25, the future value for each of the three investments, $50,000, $28,000, and $12,000, must be calculated separately using the compound interest formula and then summed together.
Step-by-step explanation:
Calculating Future Value with Compound Interest
To calculate how much Carson will have saved in his account by the end of year 25 with an average annual return of 10.5 percent, we need to consider each investment separately as they are invested at different times and will compound for different periods.
First, the $50,000 invested today will compound for 25 years. The future value (FV) for this amount can be calculated using the compound interest formula: FV = P(1 + r)n, where P is the principal amount ($50,000), r is the annual interest rate (0.105 for 10.5%), and n is the number of periods (25 years). After calculating, the future value of this investment is FV = $50,000(1 + 0.105)25.
Second, the $28,000 invested one year from today will compound for 24 years, thus the future value calculation changes to FV = $28,000(1 + 0.105)24.
Lastly, the $12,000 invested two years from today will compound for 23 years, giving us a future value of FV = $12,000(1 + 0.105)23.
To determine the total amount saved by the end of year 25, we need to sum the future values of all three investments. We carry out each of these calculations and add them together to find the total amount Carson will have saved.