It’s simple – here’s how it works: Say a community is built in Year 1. The community’s streets need to be rebuilt every 30 years. In Year 30 a new, identical community is built. Now twice the amount of taxes are coming, and so for time being the property owners only need to pay half the amount. And 30 years later, in Year 60, two new communities are built; as long as the number of properties and property taxes are doubling every 30 years, they can continue to pay half the amount.
Year 1, one community (community A), over the next 30 years is going to pay for 1 community's worth of roads (call it a 30 year loan given on day 1, let's say 1M dollars). So, the cost for community A is 1M dollars for 30 community-years of roads.
Year 30, we add a new community B to the mix. This community needs its own roads, so it needs a loan for 1M dollars it will pay off over the next 30 years. However, community A's roads have worn out. Community A just finished paying off their first loan, so they'll need a new one.
At year 60, we have paid 3M dollars, and gotten 90 "community-years" of roads out of it. This is no different than the equivalent end of the first year with one community, one loan, and 30 "community-years" of roads.
What am i missing from this example?