Find the amount of a continuous money flow in which $175 per year is being invested at 8%, compounded continuously for 20 years.

To find the amount of a continuous money flow, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:
A = the amount of the continuous money flow after t years
P = the principal amount (initial investment)
e = the base of the natural logarithm (approximately 2.71828)
r = the annual interest rate (as a decimal)
t = the time in years

Given:
P = $175 per year
r = 8% = 0.08 (as a decimal)
t = 20 years

First, we need to determine the principal amount (P) for 20 years. Since $175 is being invested per year, the principal amount (P) will be the total invested over 20 years:

P = $175 * 20 = $3,500

Now we can plug these values into the formula and solve for A:

A = $3,500 * e^(0.08 * 20)

To calculate exponential values, we can use the power of e. In this case, e^(0.08 * 20) simplifies to e^(1.6).

Using a calculator or computer, we can calculate the value of e^(1.6), which is approximately 4.953032424395194.

Now, we can substitute this value back into the formula:

A = $3,500 * 4.953032424395194

A ≈ $17,332.63

Therefore, the amount of the continuous money flow after 20 years of investing $175 per year at an 8% interest rate, compounded continuously, is approximately $17,332.63.