If you make an investment of

​$4,500

and the investment loses a continuous

5%

each​ year, what will the investment be worth in

15

​years? Round to the nearest cent

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.

If you make an investment of $4,500 and the investment loses a continuous 5% each year, what will the investment be worth in 15 years? Round to the nearest cent.

Discover how to calculate the continuous decay of a $4,500 investment losing 5% annually over 15 years using the exponential decay formula. This problem explores continuous compounding and exponential functions, ideal for students in Grades 10-12. Final investment value: $2,125.65.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation