Find the amount of a continuous money flow in which $1000 per year is being invested at 5% compounded continuously for 40 years. How would I set up my equation in order to solve?
To find the amount of a continuous money flow, you can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount
P = the initial principal (in this case, the yearly investment of $1000)
e = the base of the natural logarithm (approximately 2.71828)
r = the annual interest rate (in decimal form, so 5% becomes 0.05)
t = the time period in years (40 years in this case)
Now, let's set up the equation for the given scenario:
A = 1000 * e^(0.05 * 40)
To solve for A, you can use a calculator with an exponential function:
A ≈ 1000 * 2.71828^(0.05 * 40)
A ≈ 1000 * 2.71828^2
A ≈ 1000 * 7.38906
A ≈ 7389.06
So, the amount of the continuous money flow after 40 years would be approximately $7389.06.