Rounding Bigdecimal values with 2 Decimal Places

I think that the RoundingMode you are looking for is ROUND_HALF_EVEN. From the javadoc:

Rounding mode to round towards the "nearest neighbor" unless both neighbors are equidistant, in which case, round towards the even neighbor. Behaves as for ROUND_HALF_UP if the digit to the left of the discarded fraction is odd; behaves as for ROUND_HALF_DOWN if it's even. Note that this is the rounding mode that minimizes cumulative error when applied repeatedly over a sequence of calculations.

Here is a quick test case:

BigDecimal a = new BigDecimal("10.12345");
BigDecimal b = new BigDecimal("10.12556");

a = a.setScale(2, BigDecimal.ROUND_HALF_EVEN);
b = b.setScale(2, BigDecimal.ROUND_HALF_EVEN);

System.out.println(a);
System.out.println(b);

Correctly prints:

10.12
10.13

UPDATE:

setScale(int, int) has not been recommended since Java 1.5, when enums were first introduced, and was finally deprecated in Java 9. You should now use setScale(int, RoundingMode) e.g:

setScale(2, RoundingMode.HALF_EVEN)

Add 0.001 first to the number and then call setScale(2, RoundingMode.ROUND_HALF_UP)

Code example:

public static void main(String[] args) {
    BigDecimal a = new BigDecimal("10.12445").add(new BigDecimal("0.001"));
    BigDecimal b = a.setScale(2, BigDecimal.ROUND_HALF_UP);
    System.out.println(b);
}