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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

1 answer

To calculate the interest earned for each option, we will use the formulas for simple interest and compound interest.

Option 1: Simple Interest

The formula for simple interest is:

\[ I = P \times r \times t \]

where:

  • \( I \) = interest earned
  • \( P \) = principal amount (initial investment)
  • \( r \) = annual interest rate (as a decimal)
  • \( t \) = time (in years)

For Option 1:

  • \( P = 7000 \)
  • \( r = 0.15 \)
  • \( t = 3 \)

Calculating the interest: \[ I = 7000 \times 0.15 \times 3 \] \[ I = 7000 \times 0.45 = 3150 \]

So, the interest earned for Option 1 is $3,150.

Option 2: Compound Interest

The formula for compound interest is:

\[ A = P(1 + r)^t \]

To find the interest, we first need to calculate the total amount \( A \), and then we subtract the principal \( P \):

\[ I = A - P \]

For Option 2:

  • \( P = 7000 \)
  • \( r = 0.12 \)
  • \( t = 3 \)

Calculating \( A \): \[ A = 7000(1 + 0.12)^3 \] \[ A = 7000(1.12)^3 \] Calculating \( (1.12)^3 \): \[ 1.12^3 \approx 1.404928 \]

Now calculating \( A \): \[ A \approx 7000 \times 1.404928 \approx 9834.496 \]

Now calculating the interest: \[ I = A - P \approx 9834.496 - 7000 \approx 2834.496 \]

Rounding to the nearest whole amount, the interest earned for Option 2 is $2,834.

Summary:

  • Option 1 interest earned = $3,150
  • Option 2 interest earned = $2,834
  • The best option is option number 1.

Completed Responses

  • Option 1 interest earned = $3,150
  • Option 2 interest earned = $2,834
  • The best is option number 1