A city spends an estimated $$150,000$ per year on a flood prevention project, which includes the

construction of levees and water diversion systems. If the project reduces flood damage by $15\%$ per year

for the next $5$ years, what is the future worth $($in year $5)$ of the savings from reduced damages? Assume the

interest rate is $8\%$ per year, and the average annual flood damage without the project would be $$500,000.$

Show the cash flow diagram. No tables. Use the equations.