To calculate the value of the investment after 3 years, given a yearly depreciation of 37.6%, we can use the formula for exponential decay:

$\text{Future Value} = \text{Present Value} \times (1 - \text{Depreciation Rate})^{\text{Number of Years}}$

Given:

• Present Value (initial investment) = $8,000
• Depreciation Rate = 37.6% or 0.376
• Number of Years = 3

Calculation:

1. Substitute the values into the formula: $\text{Future Value} = 8000 \times (1 - 0.376)^3$

2. Simplify the depreciation term: $1 - 0.376 = 0.624$

3. Raise $0.624$ to the power of 3: $0.624^3 \approx 0.2429$

4. Multiply by the initial investment: $8000 \times 0.2429 = 1943.20$

Answer:

After 3 years, the investment would be worth approximately $1,943.20.

Would you like further details or have any questions?

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Here are some related questions you may find interesting:

1. What would be the value if the depreciation rate changed to 30%?
2. How would the investment grow if there were a 10% appreciation each year instead?
3. What if the depreciation rate was compounded semi-annually?
4. How much would you need to invest to achieve a future value of $10,000 after 3 years with the same depreciation rate?
5. How does compounding frequency affect the future value of an investment?

Tip: When working with percentages in exponential calculations, always convert the percentage to a decimal by dividing by 100.