Let's break this down step by step.
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Initial Investment Breakdown:
- Total savings: $5000
- Investment in stocks: 60% of $5000 \[ \text{Investment in stocks} = 0.6 \times 5000 = 3000 \]
- Amount in savings account: 40% of $5000 \[ \text{Amount in savings} = 0.4 \times 5000 = 2000 \]
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Stock Investment Performance:
- In the first year, the stock increases by 9%. \[ \text{Value after Year 1} = 3000 \times (1 + 0.09) = 3000 \times 1.09 = 3270 \]
- In the second year, the stock loses 4%. \[ \text{Value after Year 2} = 3270 \times (1 - 0.04) = 3270 \times 0.96 = 3139.20 \]
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Savings Account Interest:
- The savings account earns 4.9% APR for 2 years. The formula for the amount in the savings account after 2 years is: \[ \text{Future Value} = \text{Principal} \times (1 + r)^n \]
- Where \( r = 0.049 \) (4.9%) and \( n = 2 \): \[ \text{Future Value} = 2000 \times (1 + 0.049)^2 = 2000 \times (1.049)^2 \approx 2000 \times 1.100801 = 2201.60 \]
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Total Amount After 2 Years:
- Adding the value of stocks and the savings account: \[ \text{Total Amount} = \text{Value of Stocks} + \text{Future Value of Savings} = 3139.20 + 2201.60 = 5340.80 \]
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Total Gain:
- The total gain is the total amount after 2 years minus the initial investment: \[ \text{Total Gain} = \text{Total Amount} - \text{Initial Investment} = 5340.80 - 5000 = 340.80 \]
Thus, the total gained during the 2 years is $340.80.