The formula for the future value (FV) of compound interest is:

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

Where:

• $FV$ is the future value of the investment,
• $PV$ is the present value (initial deposit),
• $r$ is the annual interest rate (as a decimal),
• $n$ is the number of compounding periods per year,
• $t$ is the number of years.

Given:

• $PV = 40,000$,
• $r = 0.0475$,
• $n = 365$ (since it’s compounded daily),
• $t = 2$ years.

Now, let's plug these values into the formula:

$FV = 40,000 \left(1 + \frac{0.0475}{365}\right)^{365 \times 2}$

I'll calculate the future value for you.The value of the account after 2 years, with daily compounding at an interest rate of 4.75%, will be approximately $43,986.08.

Would you like more details or have any further questions?

Here are some related questions for you to explore:

1. How does increasing the interest rate affect the future value?
2. What would happen if the compounding period changed to monthly instead of daily?
3. How is the formula adjusted for continuous compounding?
4. How much interest is earned after 2 years in this scenario?
5. How would the future value change if the investment period was extended to 5 years?

Tip: The more frequent the compounding, the more interest you earn, even if the total time and rate remain the same!