This post by Gary the Water Guy explains How a water softener can save your family money.

The video shows the savings for a family of four that has water with twelve grains per gallon of water hardness after the installation of a water softener. If your water is harder than this or your household has more than four people your savings will be even greater!
The savings are in four categories, soap savings because in this case soft water requires almost 50% less soap you would save $400 a year.
Because you will no longer have scale building up in your hot water heater or dishwashing heating element that would save another $150 in energy costs every year.
Because all of the soap will rinse out of your clothes after washing and the fibres will no longer become brittle by being coated by hardness your clothes will last longer adding another $145 in savings.
And lastly you will save another $225 by having you dishwasher, washing machine, toilets and all taps last much longer. In fact I have had water softeners in every house I have owned and my washing machine is 30 years old and my dishwasher is 20 years old and they both work like new. My 10 year old hot water heater is totally scale free and is just as efficient as the day it was installed!
You can see that a Water Softener will save you $76 a month, but how much does it cost? A top of the line, metered Water Softener with chlorine removal, installed, with all taxes included would cost you under $38 per month! That's right, not only would the softener be FREE you would save an additional $38 per month over not having a water softener and still enjoy the additional benefits of soft water ( smoother skin, softer hair, easier to clean etc )