Financial part of the exchange at NUS is pretty clear. All the fees are clearly stated in the application. The major costs you would need to consider are housing, food, transportation and leisure/travels.
Housing: If you want to keep the living costs down and socialize with both Singaporean and international students, make sure you apply for a room on campus. Meal plan comes together with housing which is very convenient. In general, cost of student housing in Singapore is similar to Stockholm. Much depends on your needs and way of living. In case you are aiming for a luxurious apartment, there are plenty of flats you can share with other people. Costs would be significantly lower than apartments of similar standard in Stockholm. You can find some offers on easyroommate.com.sg!
Food: Forget about your IKEA lunch box and the microwave oven! Singapore is a paradise when it comes to food options and prices. Lunches and dinners are also very important parts of the local culture. If you eat in local canteens and food courts your lunch should cost you around 5 SGD, which is less than 30 SEK! Dinners are a bit more expensive. I recommend trying local hawker centers which offer a variety of cheap local food.