Bot GPT 4-o mini To determine which account Aerial should choose, we will calculate the total amount she would have in each account after 4 years.
Account A:
Account A pays 5.5% simple interest.
The formula for simple interest is: \[ \text{Total Amount} = \text{Principal} + (\text{Principal} \times \text{Rate} \times \text{Time}) \]
Calculation for Account A:
- Principal: \( P = 5500 \)
- Rate: \( r = 5.5% = 0.055 \)
- Time: \( t = 4 \) years
\[ \text{Total Amount} = 5500 + (5500 \times 0.055 \times 4) \]
Calculating the interest: \[ \text{Interest} = 5500 \times 0.055 \times 4 = 5500 \times 0.22 = 1210 \]
Now adding the interest to the principal: \[ \text{Total Amount} = 5500 + 1210 = 6710 \]
Account B:
Account B pays 4.5% simple interest for 3 years and then opens a bonus account with $250.
Calculation for the initial account (first 3 years):
- Rate: \( r = 4.5% = 0.045 \)
- Time: \( t = 3 \) years
\[ \text{Total Amount (Year 3)} = 5500 + (5500 \times 0.045 \times 3) \]
Calculating the interest for the first 3 years: \[ \text{Interest} = 5500 \times 0.045 \times 3 = 5500 \times 0.135 = 742.5 \]
Adding this interest: \[ \text{Total Amount (Year 3)} = 5500 + 742.5 = 6242.5 \]
Now, at the end of year 3, a bonus account of $250 is opened that earns 4.5% for 1 more year.
Calculation for the bonus account for 1 additional year (from Year 3 to Year 4):
- Principal for the bonus account: \( 250 \)
- Rate: \( 0.045 \)
- Time: \( t = 1 \) year
Calculating interest for the bonus account: \[ \text{Interest (Bonus Account)} = 250 \times 0.045 \times 1 = 11.25 \]
Adding this to the bonus account: \[ \text{Total in Bonus Account} = 250 + 11.25 = 261.25 \]
Now, adding the total from the initial account (after 4 years) and the bonus amount: \[ \text{Total Amount (after 4 years)} = 6242.5 + 261.25 = 6503.75 \]
Conclusion:
- Total from Account A = $6710
- Total from Account B = $6503.75
Thus, Account A is the better choice, earning her $206.25 more than Account B.
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