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
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