This problem demonstrates how to use the TVM Solver (Time Value of Money Solver) that can be found on many graphing calculators.
Use the TVM Solver below to answer the question.

You deposit $6,000.00 in an account that pays 4% interest compounded quarterly. How much will be in the account after 10 years?

The account balance after 10 years is 
.

To determine the answer you must first enter the values that you know in the TVM boxes below:

N:= 40 (10 * 4)    I:%= 4    PV:= -6000 (negative for money paid)    PMT:= 0 (leave it as zero)    P/Y: 4    C/Y: 4


To solve this problem using the TVM (Time Value of Money) Solver, we'll enter the following values based on the given information:

1. **N (Number of periods)**: Since interest is compounded quarterly, there are 4 quarters per year. Over 10 years, the total number of periods is $ N = 10 \times 4 = 40 $.

2. **I (Interest rate per year)**: The interest rate given is 4%, so $ I = 4 $.

3. **PV (Present Value)**: You deposit $6,000 into the account. This is the present value, and it's entered as a negative value because it's an outgoing payment. So, $ PV = -6000 $.

4. **PMT (Payment)**: Since no additional payments are being made to the account, $ PMT = 0 $.

5. **P/Y (Payments per year)**: Since the interest is compounded quarterly, there are 4 periods per year. Thus, $ P/Y = 4 $.

6. **C/Y (Compounds per year)**: The compounding frequency is quarterly, so $ C/Y = 4 $.

Now, using the TVM solver, we need to calculate the future value (FV), which gives us the balance after 10 years.

Using the TVM formula:

\[
FV = PV \times (1 + \frac{I}{100C/Y})^{N}
\]

where:
- $ PV = -6000 $
- $ I = 4 \% $
- $ C/Y = 4 $ (quarterly compounding)
- $ N = 40 $ (10 years * 4 quarters per year)

Let's calculate this now.The account balance after 10 years will be approximately **$8,933.18**.

Would you like a breakdown of the steps or further clarification? 

Here are some additional questions for practice:
1. What would the balance be if the interest were compounded annually instead of quarterly?
2. How would the final balance change if the interest rate increased to 5%?
3. What is the total interest earned after 10 years with the initial deposit of $6,000?
4. How would the balance change if you made an additional quarterly deposit of $500?
5. What happens to the future value if you withdraw $1,000 after 5 years?

**Tip**: Always double-check the compounding periods (P/Y and C/Y) when using a TVM solver!

You deposit $6,000.00 in an account that pays 4% interest compounded quarterly. How much will be in the account after 10 years?

Learn how to calculate the future value of a $6,000 deposit with 4% interest compounded quarterly over 10 years. This step-by-step guide covers key financial concepts, including compound interest and the TVM solver, and is suitable for students in Grades 10-12.

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