To calculate the total value of Kaira's investment after 3 years using the provided equation, we will first substitute \( x = 1 + r \) into the equation. The interest rate \( r \) is given as 0.0475 (or 4.75%), so we calculate \( x \).
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Calculating \( x \): \[ x = 1 + r = 1 + 0.0475 = 1.0475 \]
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Calculate \( C(x) \) using the formula provided: \[ C(x) = 600x^3 + 600x^2 + 600x \]
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Substituting \( x = 1.0475 \) into the equation and calculating each term: \[ C(1.0475) = 600(1.0475^3) + 600(1.0475^2) + 600(1.0475) \]
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First calculate \( x^3 \): \[ 1.0475^3 \approx 1.149574 \]
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Then calculate \( x^2 \): \[ 1.0475^2 \approx 1.09609 \]
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Now calculate \( x \): \[ 1.0475 \approx 1.0475 \]
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Now we can put these values into the formula:
\[ C(1.0475) \approx 600 \times 1.149574 + 600 \times 1.09609 + 600 \times 1.0475 \] \[ C(1.0475) \approx 689.6444 + 657.654 + 628.5 \] \[ C(1.0475) \approx 1965.7984 \]
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Calculating total deposits: Kaira made a deposit of $600 at the beginning of each of the 3 years: \[ \text{Total deposits} = 600 \times 3 = 1800 \]
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Calculating interest earned: The interest earned is the difference between the total value of the investment and the total deposits: \[ \text{Interest} = C(1.0475) - \text{Total deposits} \] \[ \text{Interest} \approx 1965.7984 - 1800 = 165.7984 \]
Rounding to two decimal places, the amount of interest that Kaira will earn at the end of the 3-year term is approximately: \[ \boxed{165.80} \]
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