For the past 3 years, Kaira has deposited $600 at the beginning of each year into an investment account with an interest rate of 4.75%. Use x=1+r, where r is the interest rate, and the equation C(x)=600x3+600x2+600x. The equation represents the relationship between C(x), the value of the investment after 3 years. Given that the amount of interest earned is the difference between the total value of the investment after 3 years and the sum of her $600 depositsl, find the amount of interest that Kaira will earn at the end of the 3-year term. Round the answer to two decimal places.(1 point)

Question

For the past 3 years, Kaira has deposited $600 at the beginning of each year into an investment account with an interest rate of 4.75%. Use x=1+r, where r is the interest rate, and the equation C(x)=600x3+600x2+600x. The equation represents the relationship between C(x), the value of the investment after 3 years. Given that the amount of interest earned is the difference between the total value of the investment after 3 years and the sum of her $600 depositsl, find the amount of interest that Kaira will earn at the end of the 3-year term. Round the answer to two decimal places.(1 point)

The amount of interest that Kaira will earn at the end of the 3-year term is $__

Answer 1

To find the amount of interest that Kaira will earn at the end of the 3-year term, we need to calculate the total value of the investment after 3 years and subtract the sum of her $600 deposits.

The equation C(x)=600x^3+600x^2+600x represents the value of the investment after 3 years.

To calculate C(x), we substitute x=1+r (where r is the interest rate) into the equation:
C(x)=600(1+r)^3+600(1+r)^2+600(1+r)

Simplifying the equation:
C(x)=600(1+r)^3+600(1+r)^2+600(1+r)
C(x)=600(1+3r+3r^2+r^3)+600(1+2r+r^2)+600(1+r)
C(x)=600+1800r+1800r^2+600r^3+600+1200r+600r^2+600+600r
C(x)=4800+4200r+3000r^2+600r^3

The total value of the investment after 3 years is C(x)=4800+4200r+3000r^2+600r^3.

Now, we can find the amount of interest by subtracting the sum of her $600 deposits from the total value of the investment after 3 years:
Interest = C(x)-(3*600)
Interest = (4800+4200r+3000r^2+600r^3)-(3*600)
Interest = 4800+4200r+3000r^2+600r^3-1800
Interest = 3000+4200r+3000r^2+600r^3

We need to round the answer to two decimal places.

Answer 2

To find the amount of interest that Kaira will earn at the end of the 3-year term, we need to find the total value of the investment after 3 years and subtract the sum of her $600 deposits.

Let's evaluate the equation C(x) = 600x^3 + 600x^2 + 600x.

First, substitute x = 1 + r to represent the interest rate in terms of x.

C(x) = 600x^3 + 600x^2 + 600x
C(x) = 600(1 + r)^3 + 600(1 + r)^2 + 600(1 + r)

Now let's evaluate C(x) using the given interest rate of 4.75%.

r = 0.0475
x = 1 + 0.0475

C(x) = 600(1 + 0.0475)^3 + 600(1 + 0.0475)^2 + 600(1 + 0.0475)
C(x) = 600(1.0475)^3 + 600(1.0475)^2 + 600(1.0475)
C(x) ≈ 600(1.144778) + 600(1.097068) + 600(1.0475)
C(x) ≈ 686.86680 + 658.24080 + 628.50
C(x) ≈ 1973.60760

Now, let's calculate the sum of her $600 deposits.

Sum of Deposits = $600 × 3
Sum of Deposits = $1800

Finally, to find the amount of interest, we subtract the sum of deposits from the total value of the investment.

Interest = Total Value of Investment - Sum of Deposits
Interest = $1973.60760 - $1800
Interest ≈ $173.61

Therefore, the amount of interest that Kaira will earn at the end of the 3-year term is approximately $173.61.