Suppose you found a CD that pays 3.3% interest compounded monthly for 3 years.

If you deposit $12,000 now, how much will you have in the account in 3 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 3 years. How much would you need to deposit now? (Round to the nearest cent.)


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

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

where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (the initial deposit).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times interest is compounded per year.
- $ t $ is the time the money is invested for in years.

### 1. Amount in the Account After 3 Years

Given:
- $ P = 12,000 $ dollars
- $ r = 3.3\% = 0.033 $
- $ n = 12 $ (compounded monthly)
- $ t = 3 $ years

Substitute these values into the formula:

\[
A = 12000 \left(1 + \frac{0.033}{12}\right)^{12 \times 3}
\]

Let's compute this.

### 2. Interest Earned

The interest earned can be found by subtracting the initial deposit from the total amount:

\[
\text{Interest Earned} = A - P
\]

### 3. Initial Deposit Needed to Reach $20,000 in 3 Years

To find the initial deposit needed to have $ A = 20,000 $ dollars in 3 years, we rearrange the compound interest formula to solve for $ P $:

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

Substitute the values:

\[
P = \frac{20000}{\left(1 + \frac{0.033}{12}\right)^{12 \times 3}}
\]

Let's compute these values.### Results

1. **Amount in the account after 3 years:**  
   You will have **$13,247.00** in the account.

2. **Interest earned:**  
   The interest earned over 3 years will be **$1,247.00**.

3. **Initial deposit needed to reach $20,000 in 3 years:**  
   You would need to deposit **$18,117.32** now to have $20,000 in the account in 3 years.

Would you like any further details or have any questions?

### Related Questions:
1. What would the total amount be if the interest were compounded quarterly instead of monthly?
2. How does increasing the interest rate to 4% affect the final amount after 3 years?
3. What would be the future value if the deposit was $15,000 instead of $12,000?
4. How much would be needed now to reach $25,000 in 3 years with the same interest rate?
5. What is the formula for continuously compounded interest and how would it apply here?

**Tip:** When dealing with compound interest, always check the frequency of compounding, as it can significantly impact the total amount accumulated over time.

Suppose you found a CD that pays 3.3% interest compounded monthly for 3 years. If you deposit $12,000 now, how much will you have in the account in 3 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 3 years. How much would you need to deposit now? (Round to the nearest cent.)

Learn how to calculate the future value of a $12,000 deposit in a CD with a 3.3% interest rate compounded monthly over 3 years. This detailed guide covers compound interest, the amount accumulated, the interest earned, and the initial deposit required to reach a future goal of $20,000.

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