An investment of $4,000 is deposited into an account in which interest is compounded monthly. Complete the table by filling in the amounts the investment grows to at the indicated times. (Round your answers to the nearest cent.)
r = 5%
Time (years)	Amount
1	$ 
2	$ 
3	$ 
4	$ 
5	$ 
6	$ 


To calculate the future value of an investment compounded monthly, we use the compound interest formula:

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

Where:
- $A$ is the amount of money accumulated after $t$ years, including interest.
- $P$ is the principal amount (initial investment) = $4,000.
- $r$ is the annual interest rate (in decimal) = 5% = 0.05.
- $n$ is the number of times the interest is compounded per year = 12 (for monthly compounding).
- $t$ is the number of years.

Now, we can compute the future values for each year from 1 to 6. Let's calculate that.The investment grows to the following amounts after the indicated times:

- After 1 year: **$4,204.65**
- After 2 years: **$4,419.77**
- After 3 years: **$4,645.89**
- After 4 years: **$4,883.58**
- After 5 years: **$5,133.43**
- After 6 years: **$5,396.07**

Would you like further details or explanations?

Here are five related questions for you to consider:
1. What would the future value be if the interest was compounded quarterly instead of monthly?
2. How does increasing the interest rate to 6% affect the investment after 6 years?
3. What is the formula for continuously compounded interest, and how would it apply here?
4. How much interest is earned in the 6th year alone?
5. What happens to the future value if the initial investment is increased to $5,000?

**Tip:** The more frequently interest is compounded, the greater the future value of the investment due to compounding's exponential effect.

An investment of $4,000 is deposited into an account in which interest is compounded monthly. Complete the table by filling in the amounts the investment grows to at the indicated times. (Round your answers to the nearest cent.) r = 5% Time (years) Amount 1 $ 2 $ 3 $ 4 $ 5 $ 6 $

Learn how to calculate compound interest for an investment of $4,000 with a 5% annual interest rate, compounded monthly. This detailed guide walks you through the compound interest formula, showing how the investment grows over 1 to 6 years. Suitable for Grades 9-12, including a step-by-step solution.

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