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)\nthe amount of interest that kaira will earn at the end of the 3 - year term is $ square$\ncheck answer remaining attempts : 2 view previous attempt

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)\nthe amount of interest that kaira will earn at the end of the 3 - year term is $ square$\ncheck answer remaining attempts : 2 view previous attempt

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, $(1.0475)^{3}=1.0475\times1.0475\times1.0475\approx1.1517$. $(1.0475)^{2}=1.0475\times1.0475\approx1.0973$. $C(1.0475)=600\times1.1517+600\times1.0973 + 600\times1.0475$. $C(1.0475)=600\times(1.1517 + 1.0973+1.0475)$. $C(1.0475)=600\times3.2965=1977.9$.

Step3: Calculate the total amount of deposits

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

Step4: Calculate the interest

The interest $I$ is the difference between the value of the investment and the total - amount of deposits. $I=C(1.0475)-1800$. $I = 1977.9-1800=177.90$.

Answer:

$177.90$