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I know the average saving rate in the US is ~5%, but I'm curious about the distribution. An ideal answer would be a histogram with the data broken down by what proportion of population are saving at what percentage.

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How much do people save?

enter image description here Report on the Economic Well-Being of U.S. Households in 2014, Board of Governors of the Federal Reserve System, p. 22

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About 90% of the population has very little or negative savings. The savings is driven by the upper middle class which typically saves 10% or so of pretax income. You can look at the net worth percentiles here to get a rough idea:

http://www.shnugi.com/networth-percentile-calculator/

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