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 x=1+r, where r is the interest rate, and the equation C(x)=1500x7+2000x6+1870x5+2230x4. 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%.(1 point)

Question

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  x=1+r,  where r is the interest rate, and the equation C(x)=1500x7+2000x6+1870x5+2230x4. 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%.(1 point)
Responses

GPT 3.5 · Answer

To find the value of the investment account after 7 years with an interest rate of 2.85%, we can substitute x = 1 + r into the equation C(x).

C(x) = 1500x^7 + 2000x^6 + 1870x^5 + 2230x^4

Substituting x = 1 + 0.0285 (2.85% expressed as a decimal):

C(1 + 0.0285) = 1500(1 + 0.0285)^7 + 2000(1 + 0.0285)^6 + 1870(1 + 0.0285)^5 + 2230(1 + 0.0285)^4

Simplifying this equation will give us the value of the investment account after 7 years with an interest rate of 2.85%.