Question

A bank account earns 4% interest per year. If you deposit $5,000 into the account, what will be the value of the bank account in 8 years? Round to two decimal places.(1 point)
Responses

5842.96
5842.96

6843.00
6843.00

6842.85
6842.85

73789.45

1 answer

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.