To find the amount of interest Kaira will earn at the end of the 3-year term, we need to subtract the total value of her deposits ($600 * 3 = $1800) from the total value of the investment after 3 years represented by the equation C(x).
Substituting x=1+r into the equation C(x), we get:
C(x)=(600x^3)+(600x^2)+(600x)
C(1+r)=(600(1+r)^3)+(600(1+r)^2)+(600(1+r))
C(1+r)=600(1+r)^3+600(1+r)^2+600(1+r)
C(1+r)=600(1+3r+3r^2+r^3)+600(1+2r+r^2)+600(1+r)
C(1+r)=600(1+3r+3r^2+r^3+1+2r+r^2+1+r)
C(1+r)=600(3r^3+6r^2+5r+3)
Expanding and simplifying further, we get:
C(1+r)=1800r^3+3600r^2+3000r+1800
Therefore, the total value of the investment after 3 years is given by 1800r^3+3600r^2+3000r+1800.
To find the amount of interest earned, we subtract the total value of the deposits from the total value of the investment after 3 years:
Interest = 1800r^3+3600r^2+3000r+1800 - 1800
Interest = 1800r^3+3600r^2+3000r
Now we need to substitute the given interest rate of 4.75% into the equation to calculate the interest earned:
r = 0.0475
Plugging in the value of r into the equation, we get:
Interest = 1800(0.0475)^3+3600(0.0475)^2+3000(0.0475)
Interest = 4.1306 + 8.2115 + 141.75
Interest = 154.0921
Therefore, Kaira will earn an amount of interest of $154.09 at the end of the 3-year term.
For the past 3 years, Kaira has deposited $600 at the beginning of each year into an investment account with an interest rate of 4.75%. Use x=1+r, where r is the interest rate, and the equation C(x)=600x^3+600x^2+600x. The equation represents the relationship between C(x), the value of the investment after 3 years. Given that the amount of interest earned is the difference between the total value of the investment after 3 years and the sum of her $600 depositsl, find the amount of interest that Kaira will earn at the end of the 3-year term. Round the answer to two decimal places
The amount of interest that Kaira will earn at the end of the 3-year term is $___
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