Question
Sasha makes a `\$2,400` deposit into an account that earns `4.5\%` interest compounded annually for 8 years.
Answers
GPT-4o mini
To calculate the future value of Sasha's deposit after 8 years with an interest rate of 4.5% compounded annually, we can use the formula for compound interest:
\[
A = P(1 + r)^n
\]
Where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial deposit).
- \(r\) is the annual interest rate (as a decimal).
- \(n\) is the number of years the money is invested or borrowed.
Given:
- \(P = 2400\)
- \(r = 4.5\% = 0.045\)
- \(n = 8\)
Plugging in the values:
\[
A = 2400(1 + 0.045)^8
\]
Calculating \(1 + 0.045\):
\[
1 + 0.045 = 1.045
\]
Now we calculate \(1.045^8\):
\[
1.045^8 \approx 1.432364654
\]
Now we multiply by the principal:
\[
A = 2400 \times 1.432364654 \approx 3437.68
\]
Thus, the final amount in the account after 8 years will be approximately **$3,437.68**.
\[
A = P(1 + r)^n
\]
Where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial deposit).
- \(r\) is the annual interest rate (as a decimal).
- \(n\) is the number of years the money is invested or borrowed.
Given:
- \(P = 2400\)
- \(r = 4.5\% = 0.045\)
- \(n = 8\)
Plugging in the values:
\[
A = 2400(1 + 0.045)^8
\]
Calculating \(1 + 0.045\):
\[
1 + 0.045 = 1.045
\]
Now we calculate \(1.045^8\):
\[
1.045^8 \approx 1.432364654
\]
Now we multiply by the principal:
\[
A = 2400 \times 1.432364654 \approx 3437.68
\]
Thus, the final amount in the account after 8 years will be approximately **$3,437.68**.