First, let's calculate the total value of the stocks at the end of the first year.
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Initial stock investment: \[ \text{Initial Investment} = 100 \text{ shares} \times 9.75 \text{ dollars/share} = 975 \text{ dollars} \]
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Stock gain after one year: \[ \text{Stock Gain} = 8% \text{ of } 975 \text{ dollars} = 0.08 \times 975 = 78 \text{ dollars} \]
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Total value of stocks after one year: \[ \text{Total Value of Stocks} = 975 \text{ dollars} + 78 \text{ dollars} = 1053 \text{ dollars} \]
Next, let's calculate the total value of the savings account at the end of the first year.
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Amount deposited in savings account: \[ \text{Amount} = 975 \text{ dollars} \]
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Interest earned after one year: \[ \text{Interest} = 4.5% \text{ of } 975 \text{ dollars} = 0.045 \times 975 = 43.875 \text{ dollars} \]
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Total value of savings account after one year: \[ \text{Total Value of Savings} = 975 \text{ dollars} + 43.875 \text{ dollars} = 1018.875 \text{ dollars} \]
Finally, we will calculate the difference in total value between the stocks and the savings account.
- Difference: \[ \text{Difference} = \text{Total Value of Stocks} - \text{Total Value of Savings} = 1053 \text{ dollars} - 1018.875 \text{ dollars} = 34.125 \text{ dollars} \]
Rounding to the nearest penny: \[ \text{Difference} = 34.13 \text{ dollars} \]
Thus, the difference in total value between your stocks and savings account by the end of the first year is $34.13.