Suppose you found a CD that pays 3.5% interest compounded monthly for 6 years. If you deposit $10,000 now, how much will you have in the account in 6 years? (Round to the nearest cent.) What was the interest earned? (Round to the nearest cent.) un Now suppose that you would like to have $20,000 in the account in 6 years. How much would you need to deposit now? (Round to the nearest cent.)

To solve these problems, we will use the **compound interest formula**:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $A$ is the future value of the investment/loan, including interest.
- $P$ is the principal investment amount (the initial deposit or loan amount).
- $r$ is the annual interest rate (decimal).
- $n$ is the number of times that interest is compounded per year.
- $t$ is the number of years the money is invested or borrowed for.

### 1. How much will you have in the account in 6 years if you deposit $10,000 now?

Given:
- Interest rate, $r = 3.5\%$ or $0.035$
- Compounded monthly, $n = 12$
- Time, $t = 6$ years
- Principal, $P = 10,000$

Now we can calculate the future value $A$:

\[
A = 10,000 \left(1 + \frac{0.035}{12}\right)^{12 \times 6}
\]

Let's calculate this.

The amount in the account after 6 years will be approximately **$12,333.01**.

### 2. What was the interest earned?

To find the interest earned, subtract the initial deposit from the final amount:

\[
\text{Interest Earned} = A - P = 12,333.01 - 10,000 = 2,333.01
\]

The interest earned is **$2,333.01**.

### 3. How much would you need to deposit now to have $20,000 in the account in 6 years?

Now, we rearrange the compound interest formula to solve for $P$, given that $A = 20,000$:

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

Let’s calculate this.To have $20,000 in the account in 6 years, you would need to deposit approximately **$16,216.64** now.

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Do you have any questions or would you like further details? Here are 5 related questions for further exploration:

1. How does increasing the interest rate affect the future value of the investment?
2. What would happen if the interest were compounded quarterly instead of monthly?
3. How does changing the investment period (e.g., 5 years instead of 6) alter the results?
4. What is the difference between simple interest and compound interest over 6 years?
5. How much interest would be earned if the rate increased to 5% compounded monthly?

**Tip:** Compounding more frequently (e.g., monthly vs. yearly) increases the amount of interest earned, even if the annual interest rate remains the same.

Suppose you found a CD that pays 3.5% interest compounded monthly for 6 years. If you deposit $10,000 now, how much will you have in the account in 6 years? (Round to the nearest cent.) What was the interest earned? (Round to the nearest cent.) Now suppose that you would like to have $20,000 in the account in 6 years. How much would you need to deposit now? (Round to the nearest cent.)

Learn how to calculate the future value of a CD with 3.5% interest compounded monthly over 6 years. This detailed guide explains the compound interest formula and helps determine the interest earned and initial deposit required to reach specific savings goals. Ideal for students in Grades 9-12.

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