Final answer:
John's investment's future value, accounting for reinvested dividends at a 4% annual rate with a 0% tax rate on dividends, will be approximately $24,310.12 after 5 years. The investment growth is calculated using the compound interest formula. Option A is the closest to this calculated value.
Step-by-step explanation:
The subject of this question is mathematics, specifically the concept of compound interest and its application to stock investments with dividend reinvestment. We are tasked with calculating the future value of an investment which grows by reinvesting its dividends.
The formula for compounded interest is A = P(1 + r/n)(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Given that John invested $20,000 and the stock pays annual qualifying dividends at a 4% rate, since the dividends are qualifying and John's tax rate on such dividends is 0%, the entire dividend amount can be reinvested without any deductions. Assuming the dividends are reinvested at the same 4% rate annually over 5 years, we can calculate the investment's future value without having to adjust for taxes.
Using the above information, we can calculate: A = 20,000(1 + 0.04)5 = 20,000(1.21550625) ≈ $24,310.12. The closest answer to this option is A - Approximately $24,436.