consider an investment account with a 9 - year term. the amounts of $350, $500, and $820 were deposited into…

consider an investment account with a 9 - year term. the amounts of $350, $500, and $820 were deposited into the account at the beginning of the first, fifth, and ninth years, respectively. the equation $c(x)=350x^{9}+500x^{5}+820x$ represents the relationship between $c(x)$, the value of an investment account with a 9 - year term, and its annual interest rate, $r$, where $x = 1 + r$. how much interest is earned at the end of the 9 - year term if the annual interest rate is 1.75%? (1 point)\n\n$118.30\n\n$1,788.80\n\n$1,907.55\n\n$1,670.00\n\ncheck answer\nremaining attempts : 3

consider an investment account with a 9 - year term. the amounts of $350, $500, and $820 were deposited into the account at the beginning of the first, fifth, and ninth years, respectively. the equation $c(x)=350x^{9}+500x^{5}+820x$ represents the relationship between $c(x)$, the value of an investment account with a 9 - year term, and its annual interest rate, $r$, where $x = 1 + r$. how much interest is earned at the end of the 9 - year term if the annual interest rate is 1.75%? (1 point)\n\n$118.30\n\n$1,788.80\n\n$1,907.55\n\n$1,670.00\n\ncheck answer\nremaining attempts : 3

Answer

Explanation:

Step1: Calculate the value of $x$

Given $r = 0.0175$, then $x=1 + r=1 + 0.0175 = 1.0175$.

Step2: Substitute $x$ into the function $C(x)$

$C(x)=350x^{9}+500x^{5}+820x$. $C(1.0175)=350\times(1.0175)^{9}+500\times(1.0175)^{5}+820\times(1.0175)$. First, calculate $(1.0175)^{9}\approx1.1727$, $(1.0175)^{5}\approx1.0907$. $C(1.0175)=350\times1.1727+500\times1.0907 + 820\times1.0175$. $C(1.0175)=410.445+545.35+834.35$. $C(1.0175)=1788.145$.

Step3: Calculate the total principal

The total principal is $350 + 500+820=1670$.

Step4: Calculate the interest

Interest = $C(1.0175)-$Principal. Interest = $1788.145 - 1670=118.145\approx118.30$.

Answer:

$118.30$