Find the accumulated present value of an investment over a 7 year period if there is a continuous money flow of $\mathrm{\$}8,000$ per year and the interest rate is $1.9\mathrm{\%}$ 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: $PV=C\ast (1-e^{-rt})/r$, 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 ：$\text{Math not terminated in text box}$