$1000 at 5% compounded continuously for 19 years?
What is 1000(e^((19)(.05)) ?
5%=5/100=0.05
1000*(1+0.05)^19=1000*1.05^19=
=1000*2.5269501953756382228051721572876
=2526.9501953756382228051721572876
To calculate the future value of an investment with continuous compounding, you can use the formula:
A = P * e^(rt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = the annual interest rate (expressed in decimal form)
t = the time period in years
In this case, you have an initial investment of $1000, an interest rate of 5% (or 0.05), and a time period of 19 years.
Plugging these values into the formula, we get:
A = 1000 * e^(0.05 * 19)
To solve this, we need to evaluate e^(0.05 * 19). Since we can't directly calculate e^(0.05 * 19), we can use a calculator or a math software like Python to solve it.
Using Python, you can enter the following code in the Python interpreter:
import math
A = 1000 * math.exp(0.05 * 19)
print(A)
The result will be the future value of your investment after 19 years with continuous compounding.
Note: Remember to use the decimal form of your interest rate when computing the future value. In this case, 5% is equivalent to 0.05 in decimal form.