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

Responses

$30,314.09
$30,314.09

$7,716.96
$7,716.96

$7,600.00
$7,600.00

$8,840.80

Answer 1

To find the value of the investment account after 7 years at an interest rate of 2.85%, we need to substitute the value of x into the equation C(x).

First, we need to calculate the value of x. Since x = 1 + r, and r = 2.85%, we have:
x = 1 + 0.0285
x = 1.0285

Now, we substitute x into the equation C(x):
C(x) = 1500x^7 + 2000x^6 + 1870x^5 + 2230x^4
C(1.0285) = 1500(1.0285)^7 + 2000(1.0285)^6 + 1870(1.0285)^5 + 2230(1.0285)^4

Using a calculator, we find that C(1.0285) is approximately:
C(1.0285) ≈ $7,716.96

Therefore, the value of the investment account after 7 years at an interest rate of 2.85% is $7,716.96.