Question

Determine the interest earned and the final amount in an account that begins with a $10,000 investment. It earns 4.75% simple interest for 13 years. Round the answers to two decimal places. *Drag and drop the correct answer into each spot. *Remember to use your STAAR Reference Sheet for support! (2 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. The accrued interest is $ , and the final amount in the account at the end of the 13 years is $ .

Answer 1

To calculate the interest earned and the final amount in an account using simple interest, you can use the following formulas:

1. Simple Interest (I): \[ I = P \times r \times t \] where:

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

2. Final Amount (A): \[ A = P + I \]

Given:

• \( P = 10,000 \)
• \( r = 4.75% = \frac{4.75}{100} = 0.0475 \)
• \( t = 13 \)

Now, calculate the interest earned:

\[ I = 10,000 \times 0.0475 \times 13 \] \[ I = 10,000 \times 0.0475 \times 13 = 10,000 \times 0.6175 = 6175 \]

So, the interest earned is $6,175.00.

Next, calculate the final amount:

\[ A = P + I = 10,000 + 6175 = 16175 \]

So, the final amount in the account after 13 years is $16,175.00.

Putting it all together:

• The accrued interest is $6,175.00.
• The final amount in the account at the end of the 13 years is $16,175.00.