Use the compound interest formula to compute the total amount accumulated and the interest earned.
​$2000 for 4 years at 4​% compounded quarterly
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The total amount accumulated after 4 years is ​$

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 after interest.
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time the money is invested for (in years).

Given:
- $ P = 2000 $ (initial investment),
- $ r = 4\% = 0.04 $ (annual interest rate),
- $ n = 4 $ (compounded quarterly),
- $ t = 4 $ years.

Now, let's compute the total amount:

\[
A = 2000 \left(1 + \frac{0.04}{4}\right)^{4 \times 4}
\]

Let's calculate it step-by-step.The total amount accumulated after 4 years is approximately \$2345.16.

To calculate the interest earned, we subtract the initial principal from the total amount:

\[
\text{Interest} = A - P = 2345.16 - 2000 = 345.16
\]

Thus, the interest earned is approximately \$345.16.

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What would be the total amount if the interest were compounded monthly instead of quarterly?
2. How would the total change if the interest rate was 5% instead of 4%?
3. What would be the accumulated amount if the investment period was 6 years instead of 4?
4. How much interest is earned after 4 years if the principal was \$3000 instead of \$2000?
5. If the principal was \$2000, but the interest was compounded annually, what would be the accumulated amount?

**Tip:** The more frequently interest is compounded, the more interest you accumulate, as interest is calculated on interest more often.

Use the compound interest formula to compute the total amount accumulated and the interest earned. $2000 for 4 years at 4% compounded quarterly. The total amount accumulated after 4 years is ​$?

Learn how to calculate compound interest on an initial investment of $2000 over 4 years at a 4% annual interest rate, compounded quarterly. This solution includes the compound interest formula and step-by-step calculations for the total amount accumulated and interest earned. Suitable for students in Grades 9-12.

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