Questions: Polynomial Functions Graphs Online Practice Complete this assessment to review what you've learned. It will 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 Aiyden's final amount if the annual interest rate is 4.3 percent? Round the answer to two decimal places. (1 point) 2,366.83 8,897.78 6,530.95 21,164.45 Check answer Remaining Attempts : 3

Solution Steps

To determine the final amount of Aiyden's investment, we need to construct a polynomial that represents the investment growth over 4 years with annual contributions and compound interest. The formula for the future value of an annuity with annual contributions is given by:

\[ A = P \left( \frac{(1 + r)^n - 1}{r} \right) \]

where:

• \( P \) is the annual contribution (\$2,000),
• \( r \) is the annual interest rate (4.3% or 0.043),
• \( n \) is the number of years (4).

We will use this formula to calculate the final amount.

We are given the following values:

• Annual contribution, \( P = \$2000 \)
• Annual interest rate, \( r = 0.043 \)
• Number of years, \( n = 4 \)

To find the final amount of the investment, we use the future value of an annuity formula: \[ A = P \left( \frac{(1 + r)^n - 1}{r} \right) \]

Substituting the given values into the formula, we get: \[ A = 2000 \left( \frac{(1 + 0.043)^4 - 1}{0.043} \right) \]

First, calculate \( (1 + 0.043)^4 \): \[ (1 + 0.043)^4 = 1.043^4 \approx 1.1851 \]

Next, calculate \( 1.1851 - 1 \): \[ 1.1851 - 1 = 0.1851 \]

Then, divide by \( r \): \[ \frac{0.1851}{0.043} \approx 4.3047 \]

Finally, multiply by \( P \): \[ 2000 \times 4.3047 \approx 8609.4 \]

Final Answer