Use the compound interest formula to compute the total amount accumulated and the interest earned.

​$5000

for

4

years at

2.4%

compounded monthly

The formula for compound interest is given by:

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

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

Given values:
- $P = 5000$,
- $r = 2.4\%$ or 0.024 in decimal,
- $n = 12$ (since it is compounded monthly),
- $t = 4$ years.

### Step-by-step calculation:

1. Convert the interest rate to decimal: $r = 0.024$.
2. Use $n = 12$ because the interest is compounded monthly.
3. Plug values into the formula:

\[
A = 5000 \left(1 + \frac{0.024}{12}\right)^{12 \times 4}
\]

Now let's calculate it.The total amount accumulated after 4 years is approximately **$5503.27**.

### To find the interest earned:
\[
\text{Interest Earned} = A - P = 5503.27 - 5000 = 503.27
\]
Thus, the interest earned is approximately **$503.27**.

Would you like further details or have any questions?

Here are some related questions:
1. How does increasing the interest rate affect the total accumulated amount?
2. What happens if the interest is compounded daily instead of monthly?
3. How is simple interest different from compound interest?
4. What if the investment period is extended to 10 years?
5. How do different compounding frequencies (quarterly, annually) affect the final amount?

**Tip**: The more frequently interest is compounded, the greater the total amount accumulated.

Use the compound interest formula to compute the total amount accumulated and the interest earned. $5000 for 4 years at 2.4% compounded monthly.

Learn how to compute the total accumulated amount and interest earned using the compound interest formula. In this example, $5000 is invested for 4 years at 2.4% interest compounded monthly. The total amount is approximately $5503.27, and the interest earned is $503.27. Suitable for students in Grades 9-12.

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