Daniel puts $500 in a bank for five years at 6% interest compounded annually. what is the sum after 3 years to the nearest dollar?

Suppose $r$ and $s$ are the values of $x$ that satisfy the equation \[x^2 - 2mx + (m^2+2m+3) = 0\]for some real number $m$. find the minimum real value of $r^2+s^2$.