Why private variables, while still can be accessed by accessor methods

Question

Agreed it is well defined way of encapsualtion. But i wonder how it works differently. can any one explain . We declare a varibale as private which can be accessed by accessor (set/get) methods which are usually public. so why dont we say vairbkles itself as Private ??
Pls explain

Answer 1

Not only that, but imagine the case where you have an api method, getTotal(). Your first iteratation you have something like:
double gross;
double net;
double commission;
so to get the total you may want gross - commission = net. Thus your method may look like:
public double getTotal()
return gross - commission;
But later on, iteration 2 or so, you find out you need to account for taxes, so now you don't want to break the code, the result should be the same, the NET total. However, you now need to account for taxes:
public double getTotal()
return (gross - commission) + tax;
Without breaking any code and all while maintaining the actual API definition, you have made a public accessor method provide more functionality. All code using the getTotal() method wont break nor has to be recompiled and even better it now takes into account tax.
Now, there is one "sticky" issue in the above. Because the getTotal() makes direct use of "private" variables, you may not get the "right" tax. In other words, what if there is state and local tax that need to be added? You may have two variables:
double localTax,stateTax;
The problem is, do you want your method like this:
public double getTotal()
return (gross - commission) + localTax + stateTax;
Or would it look (and possibly account for future updates) better like so:
return (gross - commission) + getTax();
The thing is, what if later on you have additional tax to handle? Sure, you can simply add it to the end, adding it, what ever. But by making a "helper" method of getTax(), you might have on iteration 2:
private double getTax()
return localTax + stateTax;
and in iteration three, you may have:
private double getTax()
return localTax + stateTax + salesTax;
Now, unless you are calling code in an intensive performance needy loop, making a couple of helper method calls won't hurt performance at all, and it will greatly enhance your code quality because you can easily change the implementation of the method(s) used, without affecting the API.