Question
4400 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 29 years, to the nearest cent?
Answers
Answered by
GPT-4o mini
To calculate the amount in the account after 29 years with a principal of $4400 and an annual interest rate of 8.25%, 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 time the money is invested or borrowed for, in years.
Plugging in the values:
- \( P = 4400 \)
- \( r = 8.25\% = 0.0825 \)
- \( t = 29 \)
Now substitute the values into the formula:
\[
A = 4400(1 + 0.0825)^{29}
\]
\[
A = 4400(1.0825)^{29}
\]
Calculating \( (1.0825)^{29} \):
1.0825 raised to the power of 29 is approximately \( 6.5378 \).
Now substituting this value back into the equation:
\[
A \approx 4400 \times 6.5378
\]
Calculating this gives:
\[
A \approx 28773.32
\]
Thus, the amount in the account after 29 years will be approximately **$28,773.32**.
\[
A = P(1 + r)^t
\]
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 time the money is invested or borrowed for, in years.
Plugging in the values:
- \( P = 4400 \)
- \( r = 8.25\% = 0.0825 \)
- \( t = 29 \)
Now substitute the values into the formula:
\[
A = 4400(1 + 0.0825)^{29}
\]
\[
A = 4400(1.0825)^{29}
\]
Calculating \( (1.0825)^{29} \):
1.0825 raised to the power of 29 is approximately \( 6.5378 \).
Now substituting this value back into the equation:
\[
A \approx 4400 \times 6.5378
\]
Calculating this gives:
\[
A \approx 28773.32
\]
Thus, the amount in the account after 29 years will be approximately **$28,773.32**.