To calculate the balance in the account after 2 years using simple interest, you can use the formula:
\[ A = P + I \] or \[ A = P(1 + rt) \]
where:
- \( A \) is the total amount of money in the account after a certain time,
- \( P \) is the principal amount (the initial deposit),
- \( r \) is the interest rate (as a decimal),
- \( t \) is the time in years,
- \( I \) is the interest earned.
Given:
- \( P = 7,912 \)
- \( r = 5.75% = 0.0575 \)
- \( t = 2 \)
Now, substitute the values into the formula:
\[ A = 7,912(1 + 0.0575 \cdot 2) \]
Calculating the interest rate for 2 years:
\[ 0.0575 \cdot 2 = 0.115 \]
Now, calculate:
\[ A = 7,912(1 + 0.115) \] \[ A = 7,912(1.115) \] \[ A \approx 7,912 \cdot 1.115 = 8,826.58 \]
Rounding to the nearest dollar, the balance in the account at the end of 2 years is approximately $8,827.
Among the choices provided, the amount closest to this calculation is $8,822.