The game aims at total realism, considering that I think it's rather fast actually. In a year you can easily more than double your population.
I don't think it's a very good idea to save up for 5 of every building though. From my experience you don't need more than 2-3 clinics, schools, etc. before their effects end up being more of a burden on your budget than contributing to it.
Also, instead of saving up that much, you could progress faster if you spent it as you got it as the first few schools, police stations etc. will increase your income if you recruit the optimal number of people.