$($Inflation$-$protected contract$)$ You are considering an investment opportunity. It requires you to pay $$20,000$ as an initial investment and will pay $$5,000$ for the next five years. If you think the proper discount rate for this project is $7\%,$ and you expect the inflation rate would be $2\%$ per year.

What is the inflation$-$protected nominal interest rate?

What would be the PV of this project?

Will you take on the project?