Final answer:
The student's question involves calculating the final value of an initial investment after five years using the compound interest formula. With an initial investment of $20,000 and a 9% annual interest rate compounded annually, the final value is $30,861.33, which does not match the provided options.
Step-by-step explanation:
The calculation to find the final value of an initial investment growing at a compound interest rate involves using the compound interest formula: Final Value = P(1 + r/n)^(nt), where P is the principal amount (initial investment), r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years. Assuming the interest is compounded annually for the given scenario:
- Initial Investment (P): $20,000
- Annual Interest Rate (r): 9% or 0.09
- Number of Times Compounded Per Year (n): 1 (annually)
- Number of Years (t): 5
Applying these values to the formula, we get: Final Value = $20,000(1 + 0.09/1)^(1*5), which simplifies to Final Value = $20,000(1 + 0.09)^5. Calculating this value gives us the final value of the investment after five years.
Using a calculator, the formula yields the final value: $20,000(1.09)^5 which equals $30,861.33, but since this amount is not an option, it may indicate the need to reinvestigate the provided options or the accuracy of the calculation.