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)
Responses

$6,530.95
$6,530.95

$2,366.83
$2,366.83

$8,897.78
$8,897.78

$21,164.45

1 answer

To determine Aiyden's final amount at the end of the 4-year term, we can use the formula for the future value of an annuity:

\[A = \frac{P \cdot (x^n - 1)}{x - 1}\]

Where:
A = final amount
P = annual investment amount
x = 1 + r (annual interest rate combined annually)
n = number of years

In this case, Aiyden is investing $2,000 each year for 4 years, and the annual interest rate is 4.3% (0.043).

So we have:
P = 2,000
r = 0.043
x = 1 + 0.043 = 1.043
n = 4

Plugging these values into the formula:

\[A = \frac{2000 \cdot (1.043^4 - 1)}{1.043 - 1}\]

Simplifying:

\[A \approx 6530.95\]

Therefore, Aiyden's final amount is approximately $6,530.95.

The correct response is:

$6,530.95