Aerial's grandmother gave her $5,500.00 to save for her college education. She went to the bank to open a savings account. The bank told her they had two options available. Account A will pay 5.5% simple interest until the account is closed. Account B will pay 4.5% simple interest and if the account is left open for longer than 3 years, then at the end of the third year a bonus account will be opened with $250 that also earns 4.5% for the remainder of the time the initial account is open. When the initial account is closed, the bonus account will be closed as well and the money from the two accounts will be combined. If Aerial is planning on leaving the money in the account for 4 years and then withdrawing all funds, then account is the better choice earning her more.

Answer 1

To determine which account will earn Aerial more money after 4 years, we'll need to calculate the total amount from both Account A and Account B after that time.

Account A:

Account A offers a simple interest rate of 5.5%. The formula for calculating simple interest is:

\[ \text{Total Amount} = \text{Principal} + \text{Interest} \] \[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]

Let's calculate the total amount for Account A after 4 years:

• Principal: $5,500.00
• Interest Rate: 5.5% (0.055)
• Time: 4 years

Interest Calculation

\[ \text{Interest} = 5500 \times 0.055 \times 4 = 5500 \times 0.22 = 1210 \]

Total Amount

\[ \text{Total Amount} = 5500 + 1210 = 6710 \]

Account B:

Account B offers a simple interest rate of 4.5% and, after 3 years, a bonus of $250 that also earns 4.5%.

1. Interest for the first 3 years:

• Principal: $5,500.00
• Interest Rate: 4.5% (0.045)
• Time: 3 years

\[ \text{Interest} = 5500 \times 0.045 \times 3 = 5500 \times 0.135 = 742.5 \]

Total amount after 3 years (without the bonus): \[ \text{Total Amount (after 3 years)} = 5500 + 742.5 = 6242.5 \]

2. Adding the new account (bonus) of $250 after 3 years:

• Principal for the bonus account: $250
• Interest Rate: 4.5% (0.045)
• Time: 1 year (from year 3 to year 4)

\[ \text{Interest for bonus} = 250 \times 0.045 \times 1 = 250 \times 0.045 = 11.25 \]

Total amount from the bonus after 1 year: \[ \text{Total Amount (bonus)} = 250 + 11.25 = 261.25 \]

3. Total amount after 4 years for Account B: \[ \text{Total Amount (Account B)} = \text{Total Amount (after 3 years)} + \text{Total Amount (bonus)} = 6242.5 + 261.25 = 6503.75 \]

Conclusion

• Total amount from Account A after 4 years: $6,710.00
• Total amount from Account B after 4 years: $6,503.75

Thus, Account A is the better choice, as it will earn Aerial more money ($6,710.00 compared to $6,503.75).