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)
1. $8,897.78
2. $2,366.83
3. $21,164.45
4. $6,530.95
To find the final amount of Aiyden's investment at the end of the 4-year term, we need to use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
where:
FV = future value of the investment
P = annual payment or investment amount ($2,000)
r = annual interest rate combined annually (4.3% or 0.043)
n = number of years (4)
Substituting the given values into the formula, we have:
FV = $2,000 * ((1 + 0.043)^4 - 1) / 0.043
Evaluating this expression, we find:
FV ≈ $6,530.95
Therefore, Aiyden's final amount is approximately $6,530.95.
The correct answer is option 4. $6,530.95.
To calculate Aiyden's final amount at the end of the 4-year term, we need to use the formula for calculating compound interest, which is given by:
Final Amount = Principal * (1 + Interest Rate)^Number of Compounding Periods
In this case, Aiyden is investing $2,000 each year for 4 years, so the principal would be $2,000 and the number of compounding periods would be 4.
The given formula, x = 1 + r, is not applicable here, so we won't be using it.
Now, let's calculate Aiyden's final amount using the compound interest formula:
Principal = $2,000
Interest Rate = 4.3% = 0.043 (expressed as a decimal)
Number of Compounding Periods = 4
Final Amount = $2,000 * (1 + 0.043)^4
Final Amount = $2,000 * (1.043)^4
Final Amount = $2,000 * 1.1890
Final Amount ≈ $2,378
Rounding the answer to two decimal places, Aiyden's final amount at the end of the 4-year term is approximately $2,378.
Therefore, the correct option is 2. $2,366.83.
To determine Aiyden's final amount at the end of the 4-year term, we need to consider the amount he invests each year and the annual interest rate.
We can use the formula for the future value of an ordinary annuity to determine the final amount:
FV = P * [(x^n - 1) / r]
Where:
FV = Future Value (final amount)
P = Periodic payment or investment amount per period
x = 1 + r (annual interest rate combined annually)
n = Number of periods (in this case, 4 years)
r = Annual interest rate
In this case, Aiyden invests $2,000 each year and the annual interest rate is 4.3%.
So, let's calculate:
P = $2,000
r = 4.3% = 0.043
n = 4
x = 1 + 0.043 = 1.043
FV = $2,000 * [(1.043^4 - 1) / 0.043]
Calculating this expression gives us a result of approximately $8,897.78.
Therefore, Aiyden's final amount at the end of the 4-year term, if the annual interest rate is 4.3 percent, is $8,897.78.
Answer: 1. $8,897.78