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.

Question

1. The accrued interest is $( ) and the final amount in the.
2. account at the end of the 13 years is $ (. ).

Answer 1

To calculate the interest earned and the final amount for a simple interest investment, you can use the formula:

\[ \text{Interest} = P \times r \times t \]

Where:

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

Given:

• \( P = 10,000 \)
• \( r = 0.0475 \) (which is 4.75% expressed as a decimal)
• \( t = 13 \)

1. Calculate the interest earned:

\[ \text{Interest} = 10,000 \times 0.0475 \times 13 \]

\[ \text{Interest} = 10,000 \times 0.0475 \times 13 = 10,000 \times 0.6175 = 6,175 \]

So, the accrued interest is \($6,175.00\).

2. Calculate the final amount in the account at the end of 13 years:

\[ \text{Final Amount} = P + \text{Interest} \]

\[ \text{Final Amount} = 10,000 + 6,175 = 16,175 \]

So, the final amount in the account at the end of the 13 years is \($16,175.00\).

In summary:

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