To find the value of an investment that loses continuously at a rate of 5% per year over 15 years, we can use the formula for continuous compound interest decay:

$A = P \cdot e^{rt}$

Where:

• $A$ is the final amount
• $P$ is the initial investment ($4,500)
• $r$ is the rate of decay (since it's losing 5%, $r = -0.05$)
• $t$ is the time in years (15 years)
• $e$ is Euler's number (approximately 2.71828)

Let's calculate it:

$A = 4500 \cdot e^{-0.05 \cdot 15}$

Now, I'll compute the value.

The value of the investment after 15 years, with a continuous annual loss of 5%, will be approximately $2,125.65.

Would you like further details or have any questions? Here are 5 related questions for deeper exploration:

1. How does continuous decay differ from simple or compound interest decay?
2. What would the value be if the loss rate was 3% instead of 5%?
3. How does the investment value change over shorter periods, like 5 or 10 years?
4. What if the investment gained 5% continuously instead of losing it?
5. How does the formula for continuous decay apply in other real-world scenarios?

Tip: When dealing with continuous growth or decay, always remember the significance of Euler's number, $e$, in the calculation formula.