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It appears that the question involves calculating the future value of an investment using simple and compound interest formulas. Let me transcribe and solve it step by step.

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Here is the extracted question and the approach:

**Problem:**
- $ P = \$12,000 $ invested in both a simple interest and compound interest scenario.
- Simple interest rate is $ r = 5\% $ annually for $ t = 3 $ years.
- Compound interest rate is $ r = 5\% $, compounded annually for $ t = 3 $ years.

We need to calculate the total amount using both simple and compound interest.

### Simple Interest Formula:
\[
A = P(1 + rt)
\]
Where:
- $ A $ is the total amount after time $ t $.
- $ P = 12,000 $ (the principal),
- $ r = 5\% = 0.05 $,
- $ t = 3 $ years.

### Compound Interest Formula:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $ A $ is the total amount,
- $ P = 12,000 $,
- $ r = 5\% = 0.05 $,
- $ n = 1 $ (compounded annually),
- $ t = 3 $ years.

I'll now solve these.### Solution:

1. **Simple Interest:**
   \[
   A_{\text{simple}} = P(1 + rt) = 12,000 \times (1 + 0.05 \times 3) = 12,000 \times 1.15 = 13,800
   \]

2. **Compound Interest:**
   \[
   A_{\text{compound}} = P \left(1 + \frac{r}{n}\right)^{nt} = 12,000 \times \left(1 + \frac{0.05}{1}\right)^{1 \times 3} = 12,000 \times (1.05)^3 = 13,891.50
   \]

Thus, after 3 years:
- The total amount with simple interest is **\$13,800**.
- The total amount with compound interest is **\$13,891.50**.

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Do you have any questions or would you like further details on the calculations? Here are 5 related questions to explore further:

1. What would the interest amount alone be for both simple and compound interest?
2. How would the result change if the interest was compounded monthly instead of annually?
3. What if the time period was extended to 5 years instead of 3?
4. Can you calculate the effective interest rate when compounded monthly over 3 years?
5. How much more does compound interest yield compared to simple interest over 10 years?

**Tip:** Compound interest grows faster than simple interest, especially as time increases due to the effect of "interest on interest."

Calculate the future value of an investment using simple and compound interest formulas.

Learn how to calculate the future value of an investment using both simple and compound interest formulas. This guide covers key financial concepts, including exponential growth and interest calculations, suitable for high school students in Grades 10-12.

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