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The problem involves calculating the future value of a compound interest investment. The given formula for compound interest is:

\[
FV = PV \left( 1 + \frac{r}{n} \right)^{nt}
\]

Where:
- $ FV $ is the future value of the investment.
- $ PV = 40,000 $ is the present value (initial investment).
- $ r = 2.25\% $ or 0.0225 (annual interest rate as a decimal).
- $ n = 365 $ (since the interest is compounded daily).
- $ t = 3 $ years (given in the problem).

Let's calculate the future value ($ FV $) based on this formula.

I'll compute the answer for you.The future value of the investment after 3 years, with daily compounding at an annual interest rate of 2.25%, is approximately **$42,793.12**.

Let me know if you'd like more details or have further questions!

Here are five related questions you could explore:
1. How would the future value change if the interest rate were 3% instead of 2.25%?
2. What would the future value be if the money was invested for 5 years instead of 3 years?
3. How does the frequency of compounding (monthly, quarterly, etc.) affect the future value?
4. What would happen to the future value if the initial investment was $50,000?
5. How is continuous compounding different from daily compounding?

**Tip:** When calculating compound interest, increasing the number of compounding periods typically results in a higher future value!

A deposit of $40,000 is placed in a scholarship fund that earns an annual interest rate of 2.25% compounded daily. The account earns interest for 3 years. Find the future value after 3 years.

Calculate the future value of a $40,000 deposit earning 2.25% interest compounded daily over 3 years. This problem involves using the compound interest formula to find how much the investment grows over time. Suitable for high school students studying finance or algebra.

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