Give the future value of compound interest formula where FV is the future value (in dollars), PV is the present value (in dollars), r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the number of years.
FV = 
  
Incorrect: Your answer is incorrect.
A deposit of $40,000 is placed in a scholarship fund that earns an annual interest rate of 4.75% compounded daily. The account earns interest for 2 years. Determine the following values. (Assume all years have 365 days.)
PV	=	$ 40000

r	=	0.0475
 

n	=	365
 

t	=	2
 

Find the value (in dollars) of the account after 2 years. (Round your answer to the nearest cent.)
$ 

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!

A deposit of $40,000 is placed in a scholarship fund that earns an annual interest rate of 4.75% compounded daily. The account earns interest for 2 years. Determine the value of the account after 2 years.

Learn how to calculate the future value of a $40,000 investment with a 4.75% annual interest rate, compounded daily for 2 years. This detailed step-by-step solution explains how compound interest works, using the formula FV = PV * (1 + r/n)^(nt). Suitable for high school students in Grades 10-12.

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