To calculate the total balance in an account after earning simple interest, we use the formula:
\[ A = P(1 + rt) \]
where:
- \( A \) is the total amount in the account after time \( t \),
- \( P \) is the principal amount (initial deposit),
- \( r \) is the rate of interest (as a decimal),
- \( t \) is the time in years.
Given:
- \( P = 7912 \)
- \( r = 5.75% = 0.0575 \)
- \( t = 2 \) years
Now plug the values into the formula:
\[ A = 7912 \left(1 + (0.0575 \times 2)\right) \]
Calculating the interest part:
\[ 0.0575 \times 2 = 0.115 \]
Adding this to 1:
\[ 1 + 0.115 = 1.115 \]
Now substitute back into the formula:
\[ A = 7912 \times 1.115 \]
Calculating this gives:
\[ A \approx 8817.58 \]
Rounding this to the nearest dollar, the balance in the account at the end of 2 years is approximately:
\[ \boxed{8818} \]