To find the amount of interest that Kaira will earn at the end of the 3-year term, we first need to evaluate the expression for \( C(x) \) given \( x = 1 + r \), where \( r \) is the interest rate (4.75% or 0.0475).
Let's calculate \( x \):
\[ x = 1 + r = 1 + 0.0475 = 1.0475 \]
Next, we will substitute \( x \) into the equation:
\[ C(x) = 600x^3 + 600x^2 + 600x \]
Now, we'll calculate \( C(1.0475) \):
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Calculate \( x^3 \): \[ x^3 = (1.0475)^3 \approx 1.148882 \]
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Calculate \( x^2 \): \[ x^2 = (1.0475)^2 \approx 1.096829 \]
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Calculating \( C(1.0475) \): \[ C(1.0475) = 600(1.148882) + 600(1.096829) + 600(1.0475) \]
Now we compute each term:
- \( 600 \times 1.148882 \approx 689.3292 \)
- \( 600 \times 1.096829 \approx 658.0974 \)
- \( 600 \times 1.0475 \approx 628.5 \)
Next, we sum these values: \[ C(1.0475) \approx 689.3292 + 658.0974 + 628.5 \approx 1975.9266 \]
So, the total value of the investment after 3 years is approximately $1975.93.
Next, we calculate the total amount Kaira deposited over the 3 years: \[ \text{Total Deposits} = 3 \times 600 = 1800 \]
Finally, the interest earned is the difference between the total value of the investment and the total deposits: \[ \text{Interest Earned} = C(1.0475) - \text{Total Deposits} \] \[ \text{Interest Earned} \approx 1975.93 - 1800 = 175.93 \]
Thus, the amount of interest that Kaira will earn at the end of the 3-year term is approximately $175.93.
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