The Interest I after t years is given by I = Prt = P*0.02*t
Now its investment after t years is given by P + I and this should be equal to 2*P for the investment to double.
Hence, P + I = 2P. Solve for t.
Let the foot of the perpendicular be P. The coordinates of P will be P(3,(3+k)/2) since it is the midpoint of BC.
Find the gradient of BC and AP in terms of k. Since AP and BC are perpendicular, it implies that :
gradient AP x gradient BC = -1
Hence, solve the quadratic equation.