Use the compound interest formula to compute the total amount accumulated and the interest earned.
​$6000 for 3 years at 3.5​% compounded monthly
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Part 1
The total amount accumulated after 3 years is ​$
  
enter your response here.
​(Round to the nearest cent as​ needed.)

To solve this problem, we'll use the compound interest formula:

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

Where:
- $ A $ is the total amount accumulated after interest.
- $ P $ is the principal amount (initial investment), which is $6000.
- $ r $ is the annual interest rate (as a decimal), which is 3.5%, or 0.035.
- $ n $ is the number of times the interest is compounded per year, which is 12 (monthly compounding).
- $ t $ is the number of years, which is 3.

Let's plug in the values:

\[
A = 6000 \left(1 + \frac{0.035}{12}\right)^{12 \times 3}
\]

Now, let's calculate this step by step.

1. Calculate the monthly interest rate:  
   \[
   \frac{0.035}{12} = 0.00291667
   \]

2. Add 1 to the monthly interest rate:  
   \[
   1 + 0.00291667 = 1.00291667
   \]

3. Calculate the exponent $ 12 \times 3 = 36 $.

4. Raise the base to the power of 36:  
   \[
   1.00291667^{36} = 1.109557
   \]

5. Multiply by the principal:  
   \[
   6000 \times 1.109557 \approx 6657.34
   \]

So, the total amount accumulated after 3 years is **$6657.34**.

If you want to calculate the interest earned, subtract the principal from the total amount accumulated:

\[
\text{Interest} = 6657.34 - 6000 = 657.34
\]

Therefore, the interest earned is **$657.34**.

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. How does the frequency of compounding affect the total amount accumulated?
2. What would the total amount be if the interest were compounded quarterly instead of monthly?
3. How much interest is earned if the investment period is extended to 5 years?
4. What would the total amount be with a higher interest rate, say 5%, compounded monthly?
5. How does simple interest compare to compound interest for the same principal and interest rate?

**Tip:** Always check whether the interest rate is given as a percentage or a decimal when using it in formulas.

Use the compound interest formula to compute the total amount accumulated and the interest earned. $6000 for 3 years at 3.5% compounded monthly.

Calculate the total amount accumulated and interest earned on a $6000 investment for 3 years at 3.5% interest, compounded monthly. Learn how to apply the compound interest formula with step-by-step instructions. Ideal for high school students in Grades 10-12.

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