Final answer:
After reinvesting his after-tax dividends at an effective rate of 4.25% for 10 years, Adam's initial investment of $25,000 would grow to $37,935.
Step-by-step explanation:
Calculating Future Value with Reinvested Dividends
If Adam invested $25,000 in a stock paying annual dividends equal to 5% of his investment and reinvested his after-tax dividends each year, we must consider the effect of his marginal tax rate of 15% on these dividends.
Each year, he earns a dividend yield of 5%, but after paying his marginal tax, he effectively gets to reinvest 4.25% (85% of 5%).
The process of reinvesting at this effective rate is an instance of compound interest.
To calculate the future value of his investment after 10 years, we use the formula:
Future Value = Present Value x (1 + Effective Rate)^n,
where Present Value is $25,000, the Effective Rate is 4.25% (which is 0.0425 in decimal form), and n is the number of years (10).
Future Value = 25,000 x (1 + 0.0425)^10 = 25,000 x 1.5174 = $37,935
Therefore, after 10 years of reinvesting the after-tax dividends, Adam's investment would be worth $37,935.