As a foreigner, you are not allowed to purchase any 'landed properties' without special permission from the government. Exceptions (where permission are given) are only available to individuals whom made or will make 'significant contributions to the society or economy'.
Furthermore as part of the recent cooling measures, foreigners are subjected to 15% additional buyers stamp duty (ABSD) on any residential properties.
Without bank loan;
With S$100,000 you can't afford to buy any property in Singapore - not even heavily subsidized public housing.
Commercial properties costs from $300k & up. Residential properties minimally half a million - small cramp condos in sub-urban areas.
With bank loan;
Banks typically loan up to 80%
of the property value (at purchase or market price - whichever is lower). As such, you need a 20% cash upfront (since you don't have CPF). With $100k, we we looking at a property value of $500,000 or less.
You also have to consider other factors such as your age, income level and total debt (including any hire purchases, installment plans etc). Considering that you are an EP holder, your monthly income should be above $3000 and so purchasing a property of value between $500,000 shouldn't be too much of a problem.
Do note that a residential property would subject you to additional buyers stamp duty (ABSD) which would bring down your maximum value below $430,000.