Jessica, a young engineer, recently received a modest inheritance. She wants to invest this money in a long$-$term private engineering venture that promises attractive returns but also requires staged investments over the next couple of years. The investment opportunity involves joining a consortium that develops modular renewable energy systems. The project requires her to commit all of her money over the next three years, with the following expected cash flows: Initial investment of $$1,000$; additional investment of $$500$ at the end of year one, and one last investment of $$1,650$ at the end of year two. The expected cashflows are $$3,000$ and $$100,$ respectively, at the end of years one and two.a$)$ Draw the cash$-$flow diagram for this investment plan. $[3\%]$b$)$ Compute the internal rate of return $($IRR$)$ for Jessicas investment over this two$-$year period. Only use ANALYTICAL approach to find your answers. $[10\%]$c$)$ Based on your calculation in Part b$,$ should Jessica accept or reject this investment if her minimum attractive rate of return $($MARR$)$ is $20\%?[3\%]$d$)$ Complete the Present Worth vs$.$ Interest Rate for the key values you found in parts b$,$ c and d$.$ Label them accordingly. Also, draw an approximate curve that passes through all these key points. $[4\%]$