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.