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
Answers
GPT-4o mini
To calculate the future value of a bank account with compound interest, you can use the formula:
\[
A = P(1 + r)^n
\]
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).
- \(n\) is the number of years the money is invested or borrowed.
In this case:
- \(P = 5000\)
- \(r = 0.04\) (4% as a decimal)
- \(n = 8\)
Now plug in the values:
\[
A = 5000(1 + 0.04)^8
\]
\[
A = 5000(1.04)^8
\]
\[
A = 5000(1.3685696) \quad \text{(using a calculator for } 1.04^8)
\]
\[
A \approx 6842.85
\]
So, the value of the bank account in 8 years will be approximately **$6842.85**.
The correct response is **6842.85**.
\[
A = P(1 + r)^n
\]
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).
- \(n\) is the number of years the money is invested or borrowed.
In this case:
- \(P = 5000\)
- \(r = 0.04\) (4% as a decimal)
- \(n = 8\)
Now plug in the values:
\[
A = 5000(1 + 0.04)^8
\]
\[
A = 5000(1.04)^8
\]
\[
A = 5000(1.3685696) \quad \text{(using a calculator for } 1.04^8)
\]
\[
A \approx 6842.85
\]
So, the value of the bank account in 8 years will be approximately **$6842.85**.
The correct response is **6842.85**.