Looking towards the future, GreenBoat Inc. explores new investment opportunities, applying its accumulated knowledge and experience to navigate the financial and strategic complexities of expanding its business horizon. GreenBoat Inc. is interested in investing in a project $$Green Energy$.$ The required rate of return for Green Energy is expressed as the force of interest $.$ Let $$ be the number of years, we have: $=\{0\mathrm{.}06+0\mathrm{.}0028(05)0\mathrm{.}08(>5)$ Green Energy generates two costs in the early years: $$110,000$ at $=0$ and $$110,000=2$ respectively. Green Energy also earns revenue. The revenue is received continuously from $=8$ to $=12.$ The annual rate of the revenue during this period is a function of time $,$ where the rate is calculated by $$110,000$ exp $(0\mathrm{.}002).$ a$)$ Calculate the discounted payback period $($DPP$)$ of Green Energy $($to the nearest year$).$