Question
Dakota earned $3.75 in interest in Account A and $15.00 in interest in Account B after 15 months. If the simple interest rate is 2% for Account A and 3% for Account B, which account has the greater principal? Explain.
Question content area bottom
Part 1
Which account has the greater principal? Select the correct answer below and fill in the answer boxes to complete your choice.
A.
Account Upper B because the principal for Account Upper B is $
enter your response here and the principal for Account Upper A is $
enter your response here
B.
Account Upper A because the principal for Account Upper A is $
enter your response here and the principal for Account Upper B is $
enter your response here.
C.
Both accounts have the same principal. The principal for both accounts is $
enter your response here.
Question content area bottom
Part 1
Which account has the greater principal? Select the correct answer below and fill in the answer boxes to complete your choice.
A.
Account Upper B because the principal for Account Upper B is $
enter your response here and the principal for Account Upper A is $
enter your response here
B.
Account Upper A because the principal for Account Upper A is $
enter your response here and the principal for Account Upper B is $
enter your response here.
C.
Both accounts have the same principal. The principal for both accounts is $
enter your response here.
Answers
Answered by
GPT-4o mini
To determine which account has the greater principal, we can use the formula for simple interest:
\[
I = P \times r \times t
\]
where:
- \(I\) is the interest earned,
- \(P\) is the principal amount (the initial amount of money),
- \(r\) is the annual interest rate (in decimal), and
- \(t\) is the time the money is invested or borrowed for (in years).
### For Account A:
Given:
- Interest (\(I_A\)) = $3.75
- Interest rate (\(r_A\)) = 2% = 0.02
- Time (\(t\)) = 15 months = \(15/12\) years = \(1.25\) years.
Using the formula, we can solve for the principal (\(P_A\)):
\[
3.75 = P_A \times 0.02 \times 1.25
\]
Calculating the right side:
\[
3.75 = P_A \times 0.025
\]
Now solving for \(P_A\):
\[
P_A = \frac{3.75}{0.025} = 150
\]
So, the principal for Account A is **$150**.
### For Account B:
Given:
- Interest (\(I_B\)) = $15.00
- Interest rate (\(r_B\)) = 3% = 0.03
- Time (\(t\)) = 15 months = \(15/12\) years = \(1.25\) years.
Using the formula again, we can solve for the principal (\(P_B\)):
\[
15.00 = P_B \times 0.03 \times 1.25
\]
Calculating the right side:
\[
15.00 = P_B \times 0.0375
\]
Now solving for \(P_B\):
\[
P_B = \frac{15.00}{0.0375} = 400
\]
So, the principal for Account B is **$400**.
### Conclusion:
Comparing the principals:
- Principal for Account A = $150
- Principal for Account B = $400
Thus, the correct answer is:
**A. Account B because the principal for Account B is $400 and the principal for Account A is $150.**
\[
I = P \times r \times t
\]
where:
- \(I\) is the interest earned,
- \(P\) is the principal amount (the initial amount of money),
- \(r\) is the annual interest rate (in decimal), and
- \(t\) is the time the money is invested or borrowed for (in years).
### For Account A:
Given:
- Interest (\(I_A\)) = $3.75
- Interest rate (\(r_A\)) = 2% = 0.02
- Time (\(t\)) = 15 months = \(15/12\) years = \(1.25\) years.
Using the formula, we can solve for the principal (\(P_A\)):
\[
3.75 = P_A \times 0.02 \times 1.25
\]
Calculating the right side:
\[
3.75 = P_A \times 0.025
\]
Now solving for \(P_A\):
\[
P_A = \frac{3.75}{0.025} = 150
\]
So, the principal for Account A is **$150**.
### For Account B:
Given:
- Interest (\(I_B\)) = $15.00
- Interest rate (\(r_B\)) = 3% = 0.03
- Time (\(t\)) = 15 months = \(15/12\) years = \(1.25\) years.
Using the formula again, we can solve for the principal (\(P_B\)):
\[
15.00 = P_B \times 0.03 \times 1.25
\]
Calculating the right side:
\[
15.00 = P_B \times 0.0375
\]
Now solving for \(P_B\):
\[
P_B = \frac{15.00}{0.0375} = 400
\]
So, the principal for Account B is **$400**.
### Conclusion:
Comparing the principals:
- Principal for Account A = $150
- Principal for Account B = $400
Thus, the correct answer is:
**A. Account B because the principal for Account B is $400 and the principal for Account A is $150.**