Question
Sasha makes a `\$2,400` deposit into an account that earns `4.5\%` interest compounded annually for 8 years.
Fill in the table below based on the information given.
p=2400
r=0.045
t=8
interest earned:___?
Account balance:____?
Fill in the table below based on the information given.
p=2400
r=0.045
t=8
interest earned:___?
Account balance:____?
Answers
GPT-4o mini
To calculate the interest earned and the account balance after 8 years with compounded interest, 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 deposit or investment).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested or borrowed.
Given:
- \( P = 2400 \)
- \( r = 0.045 \)
- \( t = 8 \)
Now we can plug in the values to calculate the account balance \( A \):
\[
A = 2400(1 + 0.045)^8
\]
First, we compute \( (1 + 0.045) \):
\[
1 + 0.045 = 1.045
\]
Now raise \( 1.045 \) to the power of 8:
\[
1.045^8 \approx 1.432364654
\]
Now multiply by the principal \( P \):
\[
A \approx 2400 \times 1.432364654 \approx 3437.68
\]
So the account balance \( A \) after 8 years is approximately \( 3437.68 \).
Next, we need to calculate the interest earned, which is given by:
\[
\text{Interest} = A - P
\]
Calculating the interest:
\[
\text{Interest} = 3437.68 - 2400 \approx 1037.68
\]
So, we can fill in the table as follows:
- Interest earned: **$1,037.68**
- Account balance: **$3,437.68**
\[
A = P(1 + r)^t
\]
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.
Given:
- \( P = 2400 \)
- \( r = 0.045 \)
- \( t = 8 \)
Now we can plug in the values to calculate the account balance \( A \):
\[
A = 2400(1 + 0.045)^8
\]
First, we compute \( (1 + 0.045) \):
\[
1 + 0.045 = 1.045
\]
Now raise \( 1.045 \) to the power of 8:
\[
1.045^8 \approx 1.432364654
\]
Now multiply by the principal \( P \):
\[
A \approx 2400 \times 1.432364654 \approx 3437.68
\]
So the account balance \( A \) after 8 years is approximately \( 3437.68 \).
Next, we need to calculate the interest earned, which is given by:
\[
\text{Interest} = A - P
\]
Calculating the interest:
\[
\text{Interest} = 3437.68 - 2400 \approx 1037.68
\]
So, we can fill in the table as follows:
- Interest earned: **$1,037.68**
- Account balance: **$3,437.68**