Yes, you shouldn’t have a problem finding a service apartment with your budget. In fact, it should be lesser.

Alternatively, you could even rent a condominium, or even consider a hotel.

Serviced Apartments are a good choice for medium-term to longer-term stays. Singapore’s serviced apartments generally offer all the amenities of 4 to 5-star Hotels, but come with the added facilities of a fully-equipped kitchen and dining area, for significantly lower rates than a Hotel room. Although many are available on a short-term basis, the savings really add up when you take a long-term lease.

It is also possible to rent rooms in private flats (check the Classifieds pages of The Straits Times for listing). Rentals differ somewhat depending on how near or far from the city centre you are. Note that the prices quoted below include all taxes.

I have a list of some best websites offering rental homes in this area with details such as location, prices, service etc.
Just email me with subject rental proerties at you dont
have to write anything.

Best wishes

Sure you can with $3K to $3.5K. Actually you can get it around $2K as long as the place not in Town area like Orchard Road.