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 3

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 3

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 the investment after 3 years

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, $(1.0475)^{3}=1.0475\times1.0475\times1.0475 = 1.150277$. $(1.0475)^{2}=1.0475\times1.0475 = 1.097256$. $C(1.0475)=600\times1.150277+600\times1.097256+600\times1.0475$ $=690.1662+658.3536 + 628.5$ $=1977.0198$.

Step3: Calculate the total of the deposits

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

Step4: Calculate the interest

The interest is the value of the investment minus the total of the deposits. Interest $=1977.0198 - 1800=177.0198\approx177.02$.

Answer:

$177.02$