Final answer:
To find the future value after 18 months for an investment of $4500 compounded continuously at an 11.22% interest rate, we use the formula S = 4500e^(0.1122*1.5), which results in a future value of approximately $5324.40.
Step-by-step explanation:
The subject of the question pertains to the calculation of the future value of an investment compounded continuously. Given the principal amount of $4500 and a continuous compound interest rate of 11.22%, we can calculate the future value, S, after 18 months. To find the amount after 18 months (1.5 years), we need to use the provided continuous compounding formula S = 4500e0.1122t, where 'e' is the base of the natural logarithm, and 't' is the time in years. The calculation is therefore S = 4500e(0.1122*1.5).
Plugging the values into the formula, we get S = 4500e(0.1122*1.5) = 4500e0.1683. Using a calculator, we find that e0.1683 ≈ 1.1832. Therefore, the future value S after 18 months is approximately 4500 * 1.1832 = $5324.40.