Those don't usually go very well.
If your population doubles, sure you need to sell enough bonds to double your infrastructure, so the annualized cost (labor + amortized capital) of providing Government Services will double. But your tax base also doubles, so as long as the new residents pay at least the average tax rate (and wealthy gentrifiers usually pay higher rates), you'll collect double the revenue and everything balances out.
To make the interest payments? A bond is a loan and it has to be paid off. The taxes from the future residents will only cover the current costs, not the interest.
(Also, the effect of interest rates is at most a small single digit percentage, so even if it's not exactly a wash, those costs could be cancelled out by other effects, e.g., the returns to scale on denser infrastructure - you can generally serve 2x the population at less than 2x the cost, but you still get to collect 2x taxes).
A new 100 unit building opens in April of year 1. 25 new students move in. This means overall the school district now needs one extra classroom. Usually the schools are at capacity already, so they need to roll in a portable and hire a teacher.
The problem lies in the fact that these kids are going to be in school in September of Year 1. Assuming it took a year to build the building, that means the district had to start spending money for the construction in year 0, and the teacher in year 1.
But the building won't get their first post-construction tax payment until Year 2. And that won't hit the school budget until Year 3.
So for 3 to 4 years, the school has had to front the costs of supporting those new students. By year 4 they'll have the revenue to support those new students, but they had to eat those first few years. And they won't hit efficiency until a few years down the line still.
If the developer has to make a direct payment to the school, it helps the absorb that cost.
As it turns out, in Cupertino at least, the developer has to pay $100 per new unit when they open the building, which at least helps offset the costs, but the school still comes out behind.