The problem asks to determine the future value of a business generating $17,000 in revenue per year over the next 5 years, with the revenue being reinvested at an interest rate of 3% per year, compounded continuously.

The formula provided in the image to calculate the future value is:

$FV = 17000 \times \frac{1}{0.03} \times \left( 1 - e^{-0.15} \right) e^{0.15}$

Where:

• 17000 is the yearly revenue.
• $0.03$ is the continuous compounding rate (3%).
• $e^{-0.15}$ represents $e^{-0.03 \times 5}$, where 5 is the number of years.
• $e^{0.15}$ is $e^{0.03 \times 5}$.

Let's break this down and compute it step by step:

1. Compute $e^{-0.15}$: $e^{-0.15} \approx 0.8607$

2. Compute $1 - e^{-0.15}$: $1 - 0.8607 = 0.1393$

3. Multiply by $e^{0.15}$ (since $e^{0.15} \approx 1.1618$): $0.1393 \times 1.1618 = 0.1619$

4. Now, multiply by $\frac{1}{0.03}$: $0.1619 \times \frac{1}{0.03} = 5.3967$

5. Finally, multiply by 17000: $17000 \times 5.3967 = 91,744.07$

Thus, the future value of the revenue stream is approximately $91,744.07.

Would you like further clarification or details on any step? Let me know if you'd like to explore this in more depth.

Here are 5 related questions to consider:

1. How does continuous compounding differ from simple compounding?
2. What happens if the interest rate increases from 3% to 4%?
3. How would the result change if the revenue was not reinvested?
4. What is the significance of the exponential term $e^{-0.15}$?
5. How can we model this problem for non-continuous reinvestment?

Tip: When dealing with continuously compounded interest, always remember that the formula involves the exponential function $e^{rt}$, which grows faster than simple compounding!