\(r=\frac{\dot{q_\theta}}{q_\theta}\) \(r=\frac{1}{\theta ln(\theta)}\) \(\theta ln{\theta}=\frac{1}{r}\)
When \(r=0.02\), using Newton's Method, \(\theta \approx 17.84\) which is the optimal duration.
\(q_0 + q_\theta e^{-r \theta}=-1 +ln(17.84) e^{-0.02 (17.84)}\)\(\approx 1.02\) (the value of the project)
When \(r=0.06\), using Newton's Method, \(\theta \approx 8.01\) which is again the optimal duration.
\(q_0 + q_\theta e^{-r \theta}=-1 +ln(8.01) e^{-0.06 (8.01)}\)\(\approx 0.29\) (the value of the project)