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The image shows a compound interest problem in a lesson on the Time Value of Money (TVM) Solver. Here's a summary of the problem:

### Problem Statement:
- You deposit $6,000.00 in an account that pays 9% interest compounded quarterly.
- You need to determine the account balance after 12 years.

### Variables provided:
- $ N $ (Number of periods): 48
- $ I\% $ (Interest rate per period): 9% (Annual)
- $ PV $ (Present Value): -6000 (negative because it's a payment/deposit)
- $ PMT $ (Payment per period): 0 (no regular payments)
- $ P/Y $ (Payments per year): 4 (quarterly)
- $ C/Y $ (Compounding periods per year): 4

### Formula:
For compound interest, the future value ($ FV $) is calculated using the formula:
\[
FV = PV \times \left(1 + \frac{r}{n}\right)^{n \cdot t}
\]
Where:
- $ r $ is the annual interest rate (9% = 0.09),
- $ n $ is the number of times interest is compounded per year (quarterly = 4),
- $ t $ is the time in years (12),
- $ PV $ is the initial deposit (-6000).

Let me calculate the future value (account balance after 12 years).The future value of the account after 12 years, compounded quarterly at 9% interest, is approximately **$17,457.84**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How does the frequency of compounding affect the future value?
2. What happens if the interest rate changes to 8% instead of 9%?
3. How would the result change if the deposit was compounded monthly instead of quarterly?
4. What if regular additional payments were made during the 12 years?
5. How does inflation impact the real value of the future amount?

**Tip:** Increasing the frequency of compounding generally results in higher future values due to more frequent interest applications.

You deposit $6,000.00 in an account that pays 9% interest compounded quarterly. How much will be in the account after 12 years?

Learn how to calculate the future value of a $6000 deposit in an account that pays 9% interest compounded quarterly for 12 years. Understand the key formulas and concepts related to compound interest and the time value of money.

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