Answer:
Step-by-step explanation:
To calculate the future value of an investment, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
e = the mathematical constant approximately equal to 2.71828
r = the interest rate (as a decimal)
t = the time period in years
In this case, the principal amount (P) is $500, the interest rate (r) is 4% or 0.04 (as a decimal), and the time period (t) is 10 years.
Plugging these values into the formula, we get:
A = 500 * e^(0.04 * 10)
Now, let's calculate the value using a calculator:
A ≈ 500 * e^(0.4)
A ≈ 500 * 1.4918247
A ≈ 745.91
Therefore, $500 invested at a 4% interest rate compounded continuously would be worth approximately $745.91 after 10 years, rounded to the nearest cent.