To calculate the balance in the account after 2 years with simple interest, we can use the formula for simple interest:
\[ A = P(1 + rt) \]
where:
- \( A \) is the total amount after interest,
- \( P \) is the principal amount (the initial deposit),
- \( r \) is the rate of interest (in decimal form),
- \( t \) is the time the money is invested or borrowed for (in years).
Given:
- \( P = 7,912 \)
- \( r = 5.75% = 0.0575 \)
- \( t = 2 \)
Now, we can plug in the values:
\[ A = 7,912(1 + (0.0575 \times 2)) \] \[ A = 7,912(1 + 0.115) \] \[ A = 7,912(1.115) \] \[ A \approx 7,912 \times 1.115 \approx 8,818.78 \]
Rounding this to the nearest whole number gives approximately $8,819.
Looking at the options provided, the one closest to this amount is:
$8,822.