Use the compound interest formula to compute the total amount accumulated and the interest earned.
​$4000 for 4 years at 7​% compounded quarterly
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Part 1
The total amount accumulated after 4 years is ​$

To compute the total amount accumulated using the compound interest formula, we can use the following formula:

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

Where:
- $ A $ is the total amount accumulated (the future value),
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the number of years.

Given:
- $ P = 4000 $ (the principal),
- $ r = 7\% = 0.07 $ (the annual interest rate as a decimal),
- $ n = 4 $ (since the interest is compounded quarterly),
- $ t = 4 $ years.

Now, plug these values into the formula:

\[
A = 4000 \left(1 + \frac{0.07}{4}\right)^{4 \times 4}
\]
\[
A = 4000 \left(1 + 0.0175\right)^{16}
\]
\[
A = 4000 \left(1.0175\right)^{16}
\]

Now calculate the exponent:

\[
A = 4000 \times 1.319
\]

\[
A \approx 5276
\]

So, the total amount accumulated after 4 years is approximately **$5276**.

### Part 2: The Interest Earned
The interest earned can be calculated by subtracting the initial principal from the total amount accumulated:

\[
\text{Interest} = A - P = 5276 - 4000 = 1276
\]

So, the interest earned is approximately **$1276**.

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Would you like any further details or have any questions?

Here are 5 related questions you might find useful:
1. How would the total amount change if the interest was compounded monthly instead of quarterly?
2. What would happen to the accumulated amount if the interest rate increased to 8%?
3. How does the number of compounding periods affect the total amount?
4. What is the difference between compound interest and simple interest in this scenario?
5. How can the future value change if the investment is made for 6 years instead of 4 years?

**Tip:** Always double-check whether the interest is compounded annually, quarterly, or monthly—it significantly affects the results!

Use the compound interest formula to compute the total amount accumulated and the interest earned. $4000 for 4 years at 7% compounded quarterly.

Learn how to calculate the total accumulated amount and interest earned on a $4000 investment over 4 years at a 7% interest rate compounded quarterly. The step-by-step solution uses the compound interest formula, yielding a total of approximately $5276 with $1276 earned in interest.

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