Question 707190
We're told that "The polynomial 900x^2 + 500x represents his savings at the beginning of the third year" and "the third year with $1600 in savings", so


900x^2 + 500x = 1600


Solve for x


900x^2 + 500x = 1600


900x^2 + 500x - 1600 = 0



Use the quadratic formula to solve for x


{{{x = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x = (-(500)+-sqrt((500)^2-4(900)(-1600)))/(2(900))}}} Plug in {{{a = 900}}}, {{{b = 500}}}, {{{c = -1600}}}


{{{x = (-500+-sqrt(250000-(-5760000)))/(1800)}}}


{{{x = (-500+-sqrt(250000+5760000))/(1800)}}}


{{{x = (-500+-sqrt(6010000))/1800}}}


{{{x = (-500+sqrt(6010000))/1800}}} or {{{x = (-500-sqrt(6010000))/1800}}}


{{{x = 1.084183}}} or {{{x = -1.639739}}} <--- Use your calculator here ( solutions are approximate and not exact)


Toss out the negative solution because you can't have a negative interest rate.


So the only approximate solution is {{{x = 1.084183}}} 


So because r = x - 1 is the interest rate, we know that the interest rate is 


r = x - 1


r = 1.084183 - 1


r = 0.084183


Which is equivalent to <font color="red">8.4%</font>