To find the difference in the amount of interest earned in 30 days between the regular savings account and the 30-day CD, we will first need to determine the amounts in each account and then calculate the interest earned from each.
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Total Savings Amount: $10,943.89
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Amount in Regular Savings Account: \[ \text{Amount in savings account} = \frac{1}{4} \times 10,943.89 = 2,735.97 \]
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Amount in 30-Day CD: \[ \text{Amount in CD} = 10,943.89 - 2,735.97 = 8,207.92 \]
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Interest Earned in Regular Savings Account:
- APR = 3.5%
- Interest for 30 days (1 month) can be calculated as: \[ \text{Interest} = \text{Principal} \times \left(\frac{\text{APR}}{12}\right) \] \[ \text{Interest in savings account} = 2,735.97 \times \left(\frac{0.035}{12}\right) = 2,735.97 \times 0.00291667 \approx 7.96 \]
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Interest Earned in 30-Day CD:
- APR = 4.57%
- Interest for 30 days can be calculated similarly: \[ \text{Interest in CD} = 8,207.92 \times \left(\frac{0.0457}{12}\right) \] \[ \text{Interest in CD} = 8,207.92 \times 0.00380833 \approx 31.29 \]
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Difference in Interest Earned:
- Now we will find the difference between the interest earned in the CD and the interest earned in the savings account: \[ \text{Difference} = \text{Interest in CD} - \text{Interest in savings account} = 31.29 - 7.96 = 23.33 \]
Thus, the difference in the amount of interest earned in 30 days between the two savings instruments is $23.33.
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