for the past 3 years, kaira has deposited $600 at the beginning of each year into an investment account with…

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 deposits, find the amount of interest that kaira will earn at the end of the 3 - year term. round the answer to two decimal places. (1 point) the amount of interest that kaira will earn at the end of the 3 - year term is $

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 deposits, find the amount of interest that kaira will earn at the end of the 3 - year term. round the answer to two decimal places. (1 point) the amount of interest that kaira will earn at the end of the 3 - year term is $

Answer

Explanation:

Step1: Calculate the value of $x$

Given $r = 0.0475$, then $x=1 + r=1 + 0.0475 = 1.0475$.

Step2: Calculate the value of $C(x)$

Substitute $x = 1.0475$ into $C(x)=600x^{3}+600x^{2}+600x$. $C(1.0475)=600\times(1.0475)^{3}+600\times(1.0475)^{2}+600\times1.0475$. First, $(1.0475)^{3}=1.0475\times1.0475\times1.0475\approx1.15$. $(1.0475)^{2}=1.0475\times1.0475\approx1.0973$. $C(1.0475)=600\times1.15 + 600\times1.0973+600\times1.0475$. $C(1.0475)=600\times(1.15 + 1.0973+1.0475)$. $C(1.0475)=600\times3.2948 = 1976.88$.

Step3: Calculate the total of deposits

The total of her deposits is $600\times3=1800$.

Step4: Calculate the interest

The interest $I$ is the difference between the total value of the investment and the sum of her deposits. $I = C(x)-1800$. $I=1976.88 - 1800=176.88$.

Answer:

$176.88$