Final answer:
To find the future value of the Tyler Town Corporation's investment, one needs to apply the compound interest formula with the appropriate values for principal, interest rate, compounding frequency, and number of years. The calculation shows a different value than the provided options, implying that the options might be incorrect or that there might be a need for clarification.
Step-by-step explanation:
To calculate the future value of an investment that compounds quarterly, we use the following formula:
Future Value = Principal × (1 + (Interest Rate / Number of Compounds))^(Number of Compounds × Number of Years)
In this case, the initial principal is $12,000, the annual interest rate is 28%, and the investment compounds quarterly over 5 years. This means that the interest rate per quarter is 28% divided by 4, and the number of times the investment compounds in 5 years is 20 (5 years × 4 quarters per year).
Let's apply the formula:
Future Value = $12,000 × (1 + (0.28 / 4))^(4 × 5)
Future Value = $12,000 × (1 + 0.07)^20
Future Value = $12,000 × (1.07)^20
Future Value = $12,000 × 3.8697
Future Value = $46,436.40
Since the calculated value does not match any of the provided options, we should double-check the calculations for accuracy. If the calculation is correctly done, it may suggest an error in the provided options or the need for further clarification on the interest rate term or compounding frequency. However, as the question specifically asks for an answer and we have followed the prescribed method, theoretically $46,436.40 would be the correct answer.