Question

Angel wants to invest $7,000 for 3 years. He has two investing options.

Option 1: Investing with a 15% simple interest rate.
Option 2: Investing with a 12% annual compound interest rate.
Find the interest earned for each option to help Angel determine which investing option will give him more interest earned. Round to the nearest whole amount if needed.



*Remember to use your STAAR Reference Sheet for support!

(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Option 1 interest earned = $ Response area

Option 2 interest earned = $ Response area
The best is option number Response area

Answer 1

To find the interest earned for each option, we can use the formulas for simple interest and compound interest.

**Option 1: Simple Interest**
The formula for simple interest is:
\[ \text{Interest} = P \times r \times t \]
where:
- \( P \) is the principal amount ($7,000),
- \( r \) is the interest rate (15% or 0.15),
- \( t \) is the time in years (3 years).

Calculating the interest for Option 1:
\[ \text{Interest} = 7000 \times 0.15 \times 3 \]
\[ \text{Interest} = 7000 \times 0.45 \]
\[ \text{Interest} = 3150 \]

**Option 2: Compound Interest**
The formula for compound interest is:
\[ \text{A} = P \times (1 + r)^t \]
where:
- \( A \) is the amount after interest,
- \( P \) is the principal amount ($7,000),
- \( r \) is the interest rate (12% or 0.12),
- \( t \) is the time in years (3 years).

Calculating the total amount for Option 2:
\[ A = 7000 \times (1 + 0.12)^3 \]
\[ A = 7000 \times (1.12)^3 \]
\[ A = 7000 \times 1.404928 \] (approximately)
\[ A \approx 9824.50 \]

Now, the interest earned for Option 2 is:
\[ \text{Interest} = A - P \]
\[ \text{Interest} \approx 9824.50 - 7000 \]
\[ \text{Interest} \approx 2824.50 \]
Rounding gives us $2825.

### Summary of Interest Earned:
- Option 1 interest earned = **$3150**
- Option 2 interest earned = **$2825**

### Conclusion:
The best option is option number **1**.