as part of the development of a new subdivision, a developer has agreed to

construct a private wastewater treatment plant and to deposit sufficient money in a perpetual

trust fund to cover the $$120,000$ annual operating cost in perpetuity, and to pay for a major

renovation to the plant every $20$ years at a cost of $$1,650,000$ per renovation. The first renovation

is to take place twenty years from now. The plant itself will initially cost $$2,700,000$ to construct.

If the trust fund earns $6\%$ interest per year $($compounded annually$),$ what is the total capitalized

cost to construct the plant, fund future periodic renovations, and fund the annual operating

costs forever?