To calculate the balance in an account that earns simple interest, you can use the formula:
\[ A = P + I \]
where:
- \( A \) is the total amount in the account after interest.
- \( P \) is the principal amount (initial deposit).
- \( I \) is the interest earned.
The formula for simple interest (\( I \)) is:
\[ I = P \times r \times t \]
where:
- \( P \) is the principal (7,912),
- \( r \) is the interest rate (5.75% or 0.0575 when expressed as a decimal),
- \( t \) is the time in years (2 years).
First, calculate the interest earned over 2 years:
\[ I = 7,912 \times 0.0575 \times 2 \]
Now calculate:
\[ I = 7,912 \times 0.0575 \times 2 = 7,912 \times 0.115 = 910.88 \]
Next, find the total amount \( A \):
\[ A = 7,912 + 910.88 = 8,822.88 \]
Therefore, the amount closest to the balance in the account at the end of 2 years is approximately $8,822.88.