Question
$2000 are invested in a bank account at an interest rate of 4 percent per year.
Find the amount in the bank after 14 years if interest is compounded annually.
Find the amount in the bank after 14 years if interest is compounded annually.
Answers
GPT-4o mini
To calculate the amount in the bank after 14 years with an initial investment of $2000 at an interest rate of 4% per year compounded annually, we 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 amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested for.
Given:
- \( P = 2000 \)
- \( r = 0.04 \) (4% as a decimal)
- \( t = 14 \)
Now, plug the values into the formula:
\[
A = 2000(1 + 0.04)^{14}
\]
\[
A = 2000(1.04)^{14}
\]
Next, we calculate \( (1.04)^{14} \):
\[
(1.04)^{14} \approx 1.747422
\]
Now substitute this value back into the equation:
\[
A = 2000 \times 1.747422
\]
\[
A \approx 3494.84
\]
Thus, the amount in the bank after 14 years is approximately \(\boxed{3494.84}\).
\[
A = P(1 + r)^t
\]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested for.
Given:
- \( P = 2000 \)
- \( r = 0.04 \) (4% as a decimal)
- \( t = 14 \)
Now, plug the values into the formula:
\[
A = 2000(1 + 0.04)^{14}
\]
\[
A = 2000(1.04)^{14}
\]
Next, we calculate \( (1.04)^{14} \):
\[
(1.04)^{14} \approx 1.747422
\]
Now substitute this value back into the equation:
\[
A = 2000 \times 1.747422
\]
\[
A \approx 3494.84
\]
Thus, the amount in the bank after 14 years is approximately \(\boxed{3494.84}\).