Final answer:
The final amount after 10 years of continuous compounding at 6% interest with an initial investment of $1000 is approximately $1819.36.
Step-by-step explanation:
To find the final amount after 10 years of continuous compounding at 6% interest, we use the formula A = P * e^(rt). Here, A is the final amount, P is the principal amount (initial investment), e is the base of the natural logarithm (approximately 2.718), r is the annual interest rate, and t is the time in years. Plugging in the values, we have A = 1000 * e^(0.06 * 10). Evaluating this, we find that the final amount after 10 years is approximately $1819.36.