To calculate the value of the bank account after 8 years with an annual interest rate of 4%, you can use the formula for compound interest:
\[ A = P(1 + r)^t \]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial deposit or investment).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested or borrowed.
In this case:
- \( P = 5000 \)
- \( r = 0.04 \) (4% as a decimal)
- \( t = 8 \)
Now plug these values into the formula:
\[ A = 5000(1 + 0.04)^8 \]
Calculating \( (1 + 0.04)^8 \):
\[ (1 + 0.04)^8 = (1.04)^8 \approx 1.368569 \]
Now calculate \( A \):
\[ A = 5000 \times 1.368569 \approx 6842.85 \]
So, the value of the bank account after 8 years will be approximately $6842.85.
The correct response is 6842.85.