Find the accumulated present value of an investment over a 7 year period if there is a continuous money flow of $\$ 8,000$ per year and the interest rate is $1.9 \%$ compounded continuously.

Step 1 ：We are given a continuous money flow of $8,000 per year for a 7 year period and an interest rate of 1.9% compounded continuously. We are asked to find the accumulated present value of this investment.

Step 2 ：We can use the formula for the present value of a continuous income stream to solve this problem. The formula is: \(PV = C * (1 - e^{-rt}) / r\), where: \(PV\) is the present value, \(C\) is the continuous money flow per year, \(r\) is the interest rate per year, \(t\) is the time in years, and \(e\) is the base of the natural logarithm.

Step 3 ：Substituting the given values into the formula, we get: \(C = 8000\), \(r = 0.019\), and \(t = 7\).

Step 4 ：Calculating the present value, we get: \(PV = 52435.750691043744\).

Step 5 ：This value represents the total amount of money that would need to be invested today, at an interest rate of 1.9% compounded continuously, to generate a continuous income stream of $8,000 per year for 7 years.

Step 6 ：\(\boxed{\text{Final Answer: The accumulated present value of the investment over a 7 year period is approximately $52,435.75.}}\)