Ladies and Gents
Sound Proofing and Sound Dampening are not the same.
Sound Proofing: is when you reduce sound transmission in or out relative to a room. The only way, and I say this as a professional, the ONLY way, is to create a room within a room. The costs speculated here are wildly off the mark. Sound travels through a medium, and in the case of the studio is mostly leaked where there is air transmission, or physical transmission. What you need is some stud wall construction, using min. 9mm board, pref. 12mm board, or doubled 9mm board. The insulation really wants to be 100mm thk rockwool to give you at least 35 dB attenuation. You would need doubled doors (solid or insulated better than hollow of course), or doubled windows. If you wish to retain a single window, get them double glazed or triple glazed. Your doors need to be retrofitted so that they seal at the bottom, conventional doors you will see , do not have this. Garden patio doors, in PVC work very well. Any local contractor can do this for you at about SGD$25 - 40 per sq ft. Houses can be built for $150 per sq. foot, so please for the sake of common sense do not speculate wild figures like 40K.
Sound dampening: this merely reduces reflections in the room, and has no contribution to sound proofing.
And once and for all, egg crates are for eggs. Use your common sense, egg crates can dampen some, the same effect of curtains. They cannot sound proof anything any more than tin foil on your head can reduce alien thought broadcasts.