Brayton wants to invest his high school earnings for the next 7 years. he deposits $1,500 into an investment account at the beginning of the first year, $ 2,000 at the beginning of the second year, $1,870 at the beginning of the third year, and $2,230 at the beginning of the fourth year. Use c(x)=1500x^7+2000x^6+1870x^5+2230x^4. The equation represents the relationship between C(x) the value of the investment after 7 years and its annual interest rate,r. Find the value of the investment account if the interest rate is 2.85%.

Answer 1

To find the value of the investment account after 7 years with an interest rate of 2.85%, we need to substitute the value of x (representing the interest rate) into the equation C(x)=1500x^7+2000x^6+1870x^5+2230x^4.

First, convert the interest rate from a percentage to a decimal by dividing it by 100:
2.85% = 2.85/100 = 0.0285

Substitute x = 0.0285 into the equation:
C(0.0285) = 1500(0.0285)^7 + 2000(0.0285)^6 + 1870(0.0285)^5 + 2230(0.0285)^4

Calculate the values:
C(0.0285) ≈ 400.89 + 200.89 + 97.40 + 43.60
C(0.0285) ≈ 742.78

The value of the investment account after 7 years with an interest rate of 2.85% is approximately $742.78.