Final answer:
The value of the investment after 14 years is approximately $6,892.64.
Step-by-step explanation:
To calculate the value of an investment compounded continuously, we use the formula: A = P * e^(rt), where A is the final amount, P is the principal (initial investment), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.
In this case, the principal (P) is $4,200, the interest rate (r) is 5.1% (or 0.051 as a decimal), and the time (t) is 14 years. Plugging these values into the formula, we get: A = 4200 * e^(0.051 * 14).
Calculating this expression, we find that the value of the investment after 14 years is approximately $6,892.64.