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This problem involves computing the future value of an investment using the compound interest formula:

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

Where:
- $ A $ is the amount in the account after the interest is applied.
- $ P $ is the principal (initial investment), which is $5000 in this case.
- $ r $ is the annual interest rate as a decimal (2.4% or 0.024).
- $ n $ is the number of times the interest is compounded per year (quarterly means $ n = 4 $).
- $ t $ is the number of years the money is invested (5 years in this case).

### Step-by-step solution:

1. **Identify the variables**:
   - $ P = 5000 $
   - $ r = 0.024 $ (since 2.4% = 0.024)
   - $ n = 4 $ (compounded quarterly)
   - $ t = 5 $

2. **Substitute the values into the compound interest formula**:

\[
A = 5000 \left( 1 + \frac{0.024}{4} \right)^{4 \times 5}
\]

3. **Simplify the terms**:
   - $ \frac{0.024}{4} = 0.006 $
   - $ 4 \times 5 = 20 $

Thus, the formula becomes:

\[
A = 5000 \left( 1 + 0.006 \right)^{20} = 5000 \left( 1.006 \right)^{20}
\]

4. **Calculate $ (1.006)^{20} $**:
   Using a calculator:

\[
1.006^{20} \approx 1.12749
\]

5. **Final calculation**:

\[
A = 5000 \times 1.12749 = 5637.45
\]

Thus, the total amount in the account after 5 years, rounded to the nearest cent, is **$5637.45**.

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:
1. What would the amount be if the interest were compounded annually instead of quarterly?
2. How would the result change if the interest rate were increased to 3%?
3. What is the effective annual rate (EAR) for this investment compounded quarterly?
4. How much total interest is earned after 5 years?
5. How does the compounding frequency affect the final amount?

**Tip**: The more frequently interest is compounded, the higher the final amount will be due to the effect of compound growth.

Compute the amount in an account with $5000 principal for 5 years at 2.4% compounded quarterly.

Learn how to calculate the future value of $5000 invested for 5 years at 2.4% interest compounded quarterly. This example walks through the compound interest formula step-by-step, perfect for students in Grades 10-12.

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