Find the accumulated future value of the continuous income stream at rate $R(t)$, for the given time $T$, and interest rate $\mathrm{k}$, compounded continuously. \[ R(t)=\$ 300,000, T=20 \text { years, } k=5 \% \] The accumulated future value is $\$ \square$. (Round to the nearest ten dollars as needed.)

Step 1 ：This question is equivalent to asking, 'What is the future value of a continuous income stream of $\$300,000$ paid annually for 20 years if the interest rate is $5\%$ and compounded continuously?'

Step 2 ：The formula for the future value of a continuous income stream is given by \[FV = R(t) \times e^{kT}\]

Step 3 ：Substituting the given values into the formula, we get \[FV = \$300,000 \times e^{0.05 \times 20}\]

Step 4 ：Calculating the above expression, we get \[FV \approx \$300,000 \times e^{1} \approx \$300,000 \times 2.71828\]

Step 5 ：Therefore, the future value of the continuous income stream is approximately \[FV \approx \$300,000 \times 2.71828 \approx \boxed{\$815,484.00}\]