Question
short answer
Your teacher will grade your response to ensure you receive proper credit for your answer.
You place $4,000.00 in a bank account with an interest rate of 5.25% APR and another $2,000.00 in an account with an interest rate of 6.00% APR.
a. How much interest will be earned for each account on the original principal in 6 months?
b. What is the difference in the amount of interest earned?
c. Which account has your money working for you the best?
Be sure to include in your response:
the steps you followed to complete your computations
the final answers to each question
the mathematical reasoning for the answer to “c”
Your teacher will grade your response to ensure you receive proper credit for your answer.
You place $4,000.00 in a bank account with an interest rate of 5.25% APR and another $2,000.00 in an account with an interest rate of 6.00% APR.
a. How much interest will be earned for each account on the original principal in 6 months?
b. What is the difference in the amount of interest earned?
c. Which account has your money working for you the best?
Be sure to include in your response:
the steps you followed to complete your computations
the final answers to each question
the mathematical reasoning for the answer to “c”
Answers
GPT-4o mini
To solve this problem, we'll calculate the interest earned in each account over 6 months using the formula for simple interest:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
where:
- Principal is the initial amount of money
- Rate is the annual interest rate (in decimal form)
- Time is the time period in years
### a. Interest earned for each account in 6 months
1. **First Account**: $4,000.00 at 5.25% APR
- Convert the rate to decimal: \( 5.25\% = 0.0525 \)
- Time for 6 months is \( 0.5 \) years.
- Calculate interest:
\[
\text{Interest} = 4000 \times 0.0525 \times 0.5 = 4000 \times 0.02625 = 105
\]
- Interest for the first account: **$105.00**
2. **Second Account**: $2,000.00 at 6.00% APR
- Convert the rate to decimal: \( 6.00\% = 0.06 \)
- Calculate interest:
\[
\text{Interest} = 2000 \times 0.06 \times 0.5 = 2000 \times 0.03 = 60
\]
- Interest for the second account: **$60.00**
### b. Difference in the amount of interest earned
Difference:
\[
\text{Difference} = 105 - 60 = 45
\]
- The difference in interest earned: **$45.00**
### c. Which account has your money working for you the best?
To determine which account has the money working for you the best, we can compare the interest rates.
1. The interest rate for the first account (5.25%) compared to the second account (6.00%):
2. Since 6.00% (second account) > 5.25% (first account), the second account has a higher interest rate and earns more interest.
Therefore, the second account is the one that has your money working for you the best.
### Final Answers
a. $105.00 (first account), $60.00 (second account)
b. $45.00
c. The second account (6.00% APR) has your money working for you the best because it has a higher interest rate.
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
where:
- Principal is the initial amount of money
- Rate is the annual interest rate (in decimal form)
- Time is the time period in years
### a. Interest earned for each account in 6 months
1. **First Account**: $4,000.00 at 5.25% APR
- Convert the rate to decimal: \( 5.25\% = 0.0525 \)
- Time for 6 months is \( 0.5 \) years.
- Calculate interest:
\[
\text{Interest} = 4000 \times 0.0525 \times 0.5 = 4000 \times 0.02625 = 105
\]
- Interest for the first account: **$105.00**
2. **Second Account**: $2,000.00 at 6.00% APR
- Convert the rate to decimal: \( 6.00\% = 0.06 \)
- Calculate interest:
\[
\text{Interest} = 2000 \times 0.06 \times 0.5 = 2000 \times 0.03 = 60
\]
- Interest for the second account: **$60.00**
### b. Difference in the amount of interest earned
Difference:
\[
\text{Difference} = 105 - 60 = 45
\]
- The difference in interest earned: **$45.00**
### c. Which account has your money working for you the best?
To determine which account has the money working for you the best, we can compare the interest rates.
1. The interest rate for the first account (5.25%) compared to the second account (6.00%):
2. Since 6.00% (second account) > 5.25% (first account), the second account has a higher interest rate and earns more interest.
Therefore, the second account is the one that has your money working for you the best.
### Final Answers
a. $105.00 (first account), $60.00 (second account)
b. $45.00
c. The second account (6.00% APR) has your money working for you the best because it has a higher interest rate.