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The question is asking for the present value of an investment with future value \( F = 25,000 \) USD in 5 years, with a continuously compounded interest rate of 2.5% per annum.

The formula for present value \( P \) with continuous compounding is:

\[
P = F \cdot e^{-rt}
\]

Where:
- \( F = 25,000 \) USD (future value),
- \( r = 0.025 \) (interest rate),
- \( t = 5 \) years,
- \( e \) is Euler's number (approximately 2.71828).

Let me calculate this for you.The present value of the investment, given the continuously compounded interest rate of 2.5% over 5 years, is approximately **22,062.42 USD**.

Would you like more details on this or have any questions? Here are some related queries:

1. How does continuous compounding differ from simple compounding?
2. What happens to the present value if the interest rate increases?
3. Can continuous compounding be applied to real-world financial investments?
4. How would the present value change if the time period is extended to 10 years?
5. What role does the exponential function play in calculating continuous compounding?

**Tip:** In financial calculations, continuous compounding often leads to a slightly lower present value compared to standard compound interest for the same rate and period.

Suppose that five years from now, you will receive USD 25,000 from investing your money at the continuously compounded interest rate of 2.5% per annum. What is the present value of this investment correct to two decimal places?

Find the present value of an investment with a future value of USD 25,000, compounded continuously at 2.5% per annum for 5 years. Using the formula P = F * e^(-rt), we calculate the present value as approximately USD 22,062.42.

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