aiyden is investing $2,000 each year into a 4 - year term investment account. use $x = 1 + r$, where $r$ is…
aiyden is investing $2,000 each year into a 4 - year term investment account. use $x = 1 + r$, where $r$ is the annual interest rate combined annually, to construct a polynomial that will help aiyden determine the final amount of his investment at the end of the 4 - year term. what is aiydens final amount if the annual interest rate is 4.3 percent? round the answer to two decimal places. (1 point)\n\n$8,897.78\n\n$2,366.83\n\n$21,164.45\n\n$6,530.95
Answer
Explanation:
Step1: Analyze the investment for each year
The first - year investment of $2000$ will earn interest for 4 years, the second - year investment of $2000$ will earn interest for 3 years, the third - year investment of $2000$ will earn interest for 2 years, and the fourth - year investment of $2000$ will earn interest for 1 year. The polynomial for the final amount $A$ of the investment is $A = 2000x^{4}+2000x^{3}+2000x^{2}+2000x$, where $x = 1 + r$.
Step2: Calculate the value of $x$
Given $r=0.043$, then $x = 1 + 0.043=1.043$.
Step3: Substitute $x$ into the polynomial
$A = 2000\times(1.043)^{4}+2000\times(1.043)^{3}+2000\times(1.043)^{2}+2000\times(1.043)$. $(1.043)^{4}=1.043\times1.043\times1.043\times1.043\approx1.18029$. $(1.043)^{3}=1.043\times1.043\times1.043\approx1.13463$. $(1.043)^{2}=1.043\times1.043\approx1.08785$. $A = 2000\times1.18029+2000\times1.13463+2000\times1.08785+2000\times1.043$. $A = 2000\times(1.18029 + 1.13463+1.08785 + 1.043)$. $A = 2000\times4.44577$. $A=8891.54$.