Nah, the higher limit is only for civil service. Private you wait long long.
Civil service is actually very median.
Big 4 about 2850, can hit 3.5k with KPMG if first class honours
BB pays about 4k and above for most roles, highest i heard is 4.7k for ops analyst at goldman sachs, slowly scale down from there, even dbs pays about 4k-ish (excluding front office)
Consulting firms pay you about 3.5k to 4k average (elite boutiques will pay you between 7k to 10k) but your progression within 5-8 years will exceed 10k (accenture is 5 years if you can survive the burn)
FMCGs like Unilever and P&G pays 5k but not much career progression
Even burger king MA program pays 4.5k
Software engineers start out about 3.5k to 4k with plenty to climb, don't even start on the big tech companies like IBM, Microsoft, SAP etc, the pay starts from 5k. Demand is very big that alot of startups with decent funding are willing to pay 4k and above for software engineers
Which is why there is increasing stress on local grads to look for a job that pays more than 3k for starters. Of course, this depends alot on your degree, honours classification, experience and attitude.