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

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

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 Kaira will earn at the end of the 3-year term, we need to subtract the total value of her $600 deposits from the total value of the investment after 3 years.

The equation C(x) represents the value of the investment after 3 years:

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

To calculate the value of the investment after 3 years, we need to substitute x = 1 + r into the equation:

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

Let's simplify this equation:

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

Next, let's calculate the value of the investment after 3 years:

C(x) = 600(1.0475^3 + 1.0475^2 + 1.0475) (rounded to 4 decimal places)

C(x) = 600(1.1452 + 1.0976 + 1.0475)

C(x) = 600(3.2903)

C(x) = 1974.18

The total value of Kaira's deposits after 3 years is 3 * 600 = 1800

So, the amount of interest earned is 1974.18 - 1800 = 174.18

Therefore, Kaira will earn $174.18 of interest at the end of the 3-year term.

Answer 2

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

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

To find the total value of Kaira's deposits, we need to add up the $600 deposits she made each year for 3 years:
Total Value of Deposits = 600 + 600 + 600 = 1800

Now, we can calculate the amount of interest earned:
Interest Earned = Total Value of Investment - Total Value of Deposits

First, let's substitute x = 1 + r into the equation C(x):
C(x) = 600(1+r)^3 + 600(1+r)^2 + 600(1+r)

Simplifying the equation, we get:
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

Plugging this equation into the formula for interest earned:
Interest Earned = C(x) - Total Value of Deposits

Interest Earned = (4800 + 4200r + 3000r^2 + 600r^3) - 1800

We can now simplify and calculate the interest earned:
Interest Earned = 4800 + 4200r + 3000r^2 + 600r^3 - 1800

Interest Earned = 3000 + 4200r + 3000r^2 + 600r^3

To calculate the final answer, you need to substitute r = 0.0475 (4.75% in decimal form) into the equation and round the result to two decimal places.