Question

Over two summers, Ray saved $900 and $500. The polynomial 900x2 + 500x represents his savings at the beginning of the third year, where x is the growth factor. (The interest rate r is x - 1.) What is the interest rate he needs to start the third year with $1600 in savings?

a. 264%
b. 0.1%
c. 1.1%
d. 8.4%

Answer 1

900 x² + 500 x= 1600 /:100
9 x² + 5 x = 16
9 x² + 5 x - 16 = 0
x 1/2 =
`\frac{-5\pm \sqrt{5^(2)-4*9*16 } }{18} = (-5\pm √(25+576) )/(18)= \\ = (-5+24.52)/(18)`
x = 1.084
The interest rate:
r = x - 1 = 1.084 - 1 = 0.084 = 8.4 %
Answer: D) 8.4 %