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The rate of Retail Prices Index (RPI) inflation rose slightly from 3.0% in November to 3.1% last month, according to the Office for National Statistics.
BBC: Economy tracker: Inflation
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The Consumer Prices Index measure of inflation was 4.5% in May, and the Retail Prices Index rate was 5.2%.
BBC: Treasury committee: Bank of England's Mervyn King
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ScotRail added that it hoped to freeze off peak fares from 2013 through until the end of its franchise in 2015, provided the Retail Prices Index (RPI) measure of inflation remained below 3.5% per annum.
BBC: Scottish rail fares to rise 3.9% from January 2013
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This is because it is linked to the Retail Prices Index measure of inflation the previous September, which was 4.6%.
BBC: New tax year and changes to your benefits
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The wider Retail Prices Index measure of inflation - the one used for many pay negotiations - is already at 4.3%.
BBC: Council workers vote for strike
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These days, as inflation sinks below zero once more prices fell by 0.4% in the year to March, according to the retail-prices index (RPI), an official measure of broad inflation published on April 21st graduating with hefty debts is the norm.
ECONOMIST: Students hope for a bonus as Britain pitches into deflation
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Earlier this year, the trustees of the Airways Pension Scheme (APS) decided to stop using the retail prices index (RPI) to uprate pensions each year.
BBC: BA pensioners fight change to inflation-proofing
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Since the last set of British Rail fares were published in June 1995, inflation measured by the Retail Prices Index (RPI) has been 66%, according to research by fares expert Barry Doe for Rail Magazine.
BBC: Have train fares gone up or down since British Rail?