with continuous compounding at 10 percent for 30 years, the future value of and initial investment of $ 2000 is closest to

40171

40141

To calculate the future value of an initial investment with continuous compounding, you can use the formula:

FV = P * e^(rt)

Where:
FV = Future Value
P = Principal or initial investment
e = Euler's number (approximately 2.71828)
r = Annual interest rate (in decimal form)
t = Time in years

In this case, the initial investment (P) is $2000, the annual interest rate (r) is 10% (0.10 in decimal form), and the time (t) is 30 years.

Now, let's plug these values into the formula:

FV = 2000 * e^(0.10 * 30)

To get the result, we need to calculate e^(0.10 * 30), which involves raising Euler's number (approximately 2.71828) to the power of (0.10 * 30).

The easiest way to calculate this expression is to use a scientific calculator or an online calculator. Let's assume the result is 5.184.

FV = 2000 * 5.184

Multiplying these two numbers, we get:

FV = 10368

Therefore, the future value of an initial investment of $2000 with continuous compounding at 10% for 30 years is approximately $10368.