About $10K base is possible at a bulge bracket investment bank for a local Bachelors grad, although $6-7K is more likely. To get $10K, typically you would need to prove yourself through a previous summer internship or be a Masters/MBA local grad. You will also be competing against top foreign graduates from schools like Oxbridge, Harvard etc, so for the lucrative investment banking areas, only 1 or 2 local grads may be taken in per department. Some bulge bracket firms don't take local grads at the Bachelors level.

Investment banks do take in children of important clients so you will see some rich useless kids, but they fade pretty fast if they are no good and end up in sales/relationship roles or fired. Assuming you survive, the downside is that you are working or travelling all the time and have no social life and little sleep. Very few local grads make it beyond 3-4 years, with most falling out at about 2 years because Singaporeans by and large like their creature comforts, value their off-time and can't sustain the intense pace for very long. You also have to compete against very aggressive smart mainland Chinese and Indians in addition to a smattering of caucasian grads. Having both husband and wife working in top investment banks is typically a recipe for disaster. There are lots of divorce cases. A lot of high flying women investment bankers end up as old maids or finally marrying when they are close to 40. Its difficult to have it all....