Final answer:
To determine the value of the investment after 120 units of time, the compound interest formula is applied using a principal amount of 10,250 at a 4.12% interest rate, yielding a result of approximately 51,337.67. This value does not match any of the provided options, indicating a potential error in the question or the options.
Step-by-step explanation:
The question asks for the future value of an investment that is represented by the compound interest formula A(t) = P(1+r)^n, where A(t) is the amount of money accumulated after n units of time, including interest, P is the principal amount, r is the annual interest rate, and n is the number of times the interest is compounded per unit of time.
In this case, the principal amount P is 10,250, the interest rate r is 4.12% (expressed as 0.0412 in decimal form), and the investment is compounded 120 times. To find the value of the investment after 120 units of time, plug the values into the formula:
A = 10,250(1+0.0412)^120
To solve, we can use the calculator, and we find that the value of the account after 120 units of time is approximately 51,337.67. This amount is not exactly represented in the given options A, B, C, D, indicating a possible error in the question or the options provided.
However, if this is a theoretical multiple-choice question with an error, we would need the correct interest rate or time period that matches one of the provided options.