Final answer:
To find the value of the investment after 40 years with compound interest, use the formula A = P(1+r)^n, where P is the principal amount, r is the interest rate, and n is the number of years. Plugging in the given values, the investment would be worth approximately $2,531,234.23 after 40 years.
Step-by-step explanation:
To calculate the value of the investment after 40 years, we can use the formula for compound interest: A = P(1+r)^n, where A is the final amount, P is the principal amount (initial investment), r is the interest rate (in decimal form), and n is the number of years.
Given that the principal amount is $10,000, the interest rate is 12% (or 0.12 in decimal form), and the number of years is 40, we can plug these values into the formula:
A = 10,000(1+0.12)^40
Simplifying further:
A = 10,000(1.12)^40
Calculating the result:
A = 10,000(25.31234234)
A ≈ $2,531,234.23