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
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
To determine the final amount of Aiyden's investment at the end of the 4-year term, we can use the formula:
FV = P * (1 + r)^n
where FV is the future value or final amount, P is the yearly investment amount, r is the annual interest rate, and n is the number of years.
In this case, Aiyden is investing $2,000 each year and the annual interest rate is 4.3%.
Substituting the values into the formula:
FV = $2,000 * (1 + 0.043)^4
Calculating using a calculator:
FV ≈ $2,366.83
Therefore, Aiyden's final amount at the end of the 4-year term, with an annual interest rate of 4.3%, is approximately $2,366.83.
To determine Aiyden's final amount at the end of the 4-year term, we can use the formula for compound interest:
A = P(1+r/n)^(nt)
Where:
A = final amount
P = principal amount invested each year ($2,000)
r = annual interest rate (4.3% or 0.043 as a decimal)
n = number of times interest is compounded per year (assuming it is compounded annually, so n = 1)
t = number of years (4)
Plugging in the values into the formula:
A = 2000(1 + 0.043/1)^(1*4)
A = 2000(1 + 0.043)^4
A ≈ 2000(1.043)^4
A ≈ 2000(1.17809051)
A ≈ 2356.18
Rounding the final amount to two decimal places, we get $2,356.83. Therefore, the correct answer is:
$2,366.83