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purchase have increased 25 over this period she has in fact suffered a real loss of about 15 in her purchasing power notice that the approximation here is a bit rough since 1 1 1 25 1 0 88 1 12 the actual loss of purchasing power is exactly 12 if the inflation rate and the nominal interest are relatively low the fisher equation can be approximated by r i π e displaystyle r i pi _ e after tax real interest rate edit the real return actually gained by a lender is lower if there is a non zero tax rate imposed on interest earnings generally taxes are imposed on nominal interest earnings not adjusted for inflation if the tax rate is denoted as t the before tax nominal earning rate is i the amount of taxes paid per dollar or other unit invested is i t and so the after tax nominal earning is i 1 t hence the expected after tax real return to the investor using the simplified approximate fisher equation above is given by expected real after tax return i 1 t π e displaystyle i 1 t pi _ e variations in inflation edit the inflation rate will not be known in advance people often base their expectation of future inflation on an average of inflation rates in the past but this gives rise to errors the real interest rate ex post may turn out to be quite different from the real interest rate ex ante real interest rate that was expected in advance borrowers hope to repay in cheaper money in the future while lenders hope to collect on more expensive money when inflation and currency risks are underestimated by lenders then they will suffer a net reduction in buying power the complexity increases for bonds issued for a long term where the average inflation rate over the term of the loan may be subject to a great deal of uncertainty in response to this many governments have issued real return bonds also known as inflation indexed bonds in which the principal value and coupon rises each year with the rate of inflation with the result that the interest rate on the bond approximates a real interest rate e g the three month indexation lag of tips can result in a divergence of as much as 0 042 from the real interest rate according to research by grishchenko and huang 3 in the us treasury inflation protected securities tips are issued by the us treasury the expected real interest rate can vary considerably from year to year the real interest rate on short term loans is strongly influenced by the monetary policy of central banks the real interest rate on longer term bonds tends to be more market driven and in recent decades with globalized financial markets the real interest rates in the industrialized countries have become increasingly correlated real interest rates have been low by historical standards since 2000 due to a combination of factors including relatively weak demand for loans by corporations plus strong savings in newly industrializing countries in asia the latter has offset the large borrowing demands by the us federal government which might otherwise have put more upward pressure on real interest rates related is the concept of risk return which is the rate of return minus the risks as measured against the safest least risky investment available thus if a loan is made at 15 with an inflation rate of 5 and 10 in risks associated with default or problems repaying then the risk adjusted rate of return on the investment is 0 importance in economic theory edit effective federal funds rate and prescriptions from alternate versions of the taylor rule the amount of physical investment in particular the purchasing of new machines and other productive capacity that firms engage in partially depends on the level of real interest rates because such purchases typically must be financed by issuing new bonds if real interest rates are high the cost of borrowing may exceed the real physical return of some potentially purchased machines in the form of output produced in that case those machines will not be purchased lower real interest rates would make it profitable to borrow to finance the purchasing of a greater number of machines the real interest rate is used in various economic theories to explain such phenomena as capital flight business cycles and economic bubbles when the real rate of interest is high because demand for credit is high then the usage of income will all other things being equal move from consumption to saving and physical investment will fall conversely when the real rate of interest is low income usage will move from saving to consumption and physical investment will rise different economic theories beginning with the work of knut wicksell have had different explanations of the effect of rising and falling real interest rates thus assuming risks are constant international capital moves to markets that offer higher real rates of interest from markets that offer low or negative real rates of interest capital flows of this kind often reflect speculation in financial and foreign exchange rate markets real federal funds rate edit in setting monetary policy the u s federal reserve and other central banks uses open market operations affecting the amounts of very short term funds federal funds supplied and demanded and thus affecting the federal funds rate by targeting this at a low rate they can encourage borrowing and thus economic activity or the reverse by raising the rate like any interest rate there are a nominal and a real value defined as described above further there is a concept called the equilibrium real federal funds rate r or r star alternatively called the natural rate of interest or the neutral real rate which is the level of the real federal funds rate if allowed to prevail for several years that would place economic activity at its potential and keep inflation low and stable there are various methods used to estimate this amount using tools such as the taylor rule it is possible for this rate to be negative 4 negative real interest rates edit the real interest rate r displaystyle r can be calculated in terms of the nominal interest rate i displaystyle i and the inflation rate π displaystyle pi via the fisher equation r i π 1 π displaystyle r frac i pi 1 pi if there is a negative real interest rate it means that the inflation rate is greater than the nominal interest rate if the federal funds rate is 2 and the inflation rate is 10 then the borrower would gain 7 27 of every dollar borrowed per year 0 02 0 1 1 0 1 0 0727 displaystyle frac 0 02 0 1 1 0 1 0 0727 negative real interest rates are an important factor in government fiscal policy since 2010 the u s treasury has been obtaining negative real interest rates on government debt meaning the inflation rate is greater than the interest rate paid on the debt 5 such low rates outpaced by the inflation rate occur when the market believes that there are no alternatives with sufficiently low risk or when popular institutional investments such as insurance companies pensions or bond money market and balanced mutual funds are required or choose to invest sufficiently large sums in treasury securities to hedge against risk 6 7 lawrence summers stated that at such low rates government debt borrowing saves taxpayer money and improves creditworthiness 8 9 in the late 1940s through the early 1970s the us and uk both reduced their debt burden by about 30 to 40 of gdp per decade by taking advantage of negative real interest rates but there is no guarantee that government debt rates will continue to stay so low 6 10 between 1946 and 1974 the us debt to gdp ratio fell from 121 to 32 even though there were surpluses in only eight of those years which were much smaller than the deficits 11 see also edit real versus nominal value shadow rate a variation on the real interest rate inflation deflation is lm model macroeconomics financial repression natural rate of interest references edit marc levinson 2006 guide to financial markets the economist page 24 frb speech with slideshow bernanke long term interest rates march 1 2013 www federalreserve gov retrieved 2017 03 07 grishchenko olesya v jing zhi huang june 2012 inflation risk premium evidence from the tips market pdf finance and economics discussion series divisions of research statistics and monetary affairs federal reserve board washington d c retrieved 26 may 2013 u s federal reserve remarks by vice chairman roger w ferguson jr october 29 2004 saint louis federal reserve 2012 5 year treasury inflation indexed security constant maturity fred economic data chart from government debt auctions the x axis at y 0 represents the inflation rate over the life of the security 1 2 carmen m reinhart and m belen sbrancia march 2011 the liquidation of government debt national bureau of economic research working paper no 16893 david wessel august 8 2012 when interest rates turn upside down wall street journal full text archived 2013 01 20 at the wayback machine lawrence summers june 3 2012 breaking the negative feedback loop reuters matthew yglesias may 30 2012 why are we collecting taxes slate william h gross may 2 2011 the caine mutiny part 2 archived 2012 10 13 at the wayback machine pimco investment outlook why the u s government never ever has to pay back all its debt the atlantic february 1 2013 external links edit equilibrium real interest rate by roger ferguson 2004 on the distinction between real return and nominal bonds by peter spiro 2004 real interest rates by country via quandl v t e economic history of the united states and commonwealth of nations countries commercial revolution 1000 1760 great bullion famine c 1400 c 1500 great slump 1430 1490 the great debasement 1544 1551 financial revolution 1690 1800 slump of 1706 great frost of 1709 south sea bubble 1713 1720 mississippi bubble 1717 1720 economic impact of the seven years war 1754 1763 1st industrial revolution market revolution 1760 1870 industrial revolution scotland united states wales bengal bubble of 1769 1769 1784 british credit crisis of 1772 1773 american revolutionary war inflation 1775 1783 panic of 1785 1785 1788 copper panic of 1789 panic of 1792 1789 1793 canal mania c 1790 c 1810 panic of 1796 1797 1796 1799 1802 1804 recession carolina gold rush 1802 1825 depression of 1807 1807 1810 1810s alabama real estate bubble alabama fever 1812 recession post napoleonic depression 1815 1821 1822 23 recession panic of 1825 panic of 1826 1828 29 recession georgia gold rush 1828 c 1840 1830s chicago real estate bubble 1833 34 recession panic of 1837 1836 1838 and 1839 1843 u s state defaults in the 1840s railway mania c 1840 c 1850 plank road boom 1844 c 1855 1845 46 recession panic of 1847 1847 1848 california gold rush 1848 1855 british columbia gold rushes queen charlottes gold rush 1851 fraser canyon gold rush 1858 rock creek gold rush 1859 similkameen gold rush 1860 stikine gold rush 1861 cariboo gold rush 1861 1867 wild horse creek gold rush 1863 1870 leechtown gold rush 1864 1865 big bend gold rush c 1865 omineca gold rush 1869 victorian gold rush 1851 c 1870 new south wales gold rush 1851 1880 australian gold rushes 1851 1914 1853 54 recession panic of 1857 1857 1858 pike s peak gold rush 1858 1861 pennsylvania oil rush 1859 1891 1860 61 recession colorado river mining boom 1861 1864 otago gold rush 1861 1864 u s civil war economy 1861 1865 first nova scotia gold rush 1861 1874 west coast gold rush 1864 1867 panic of 1866 1865 1867 vermilion lake gold rush 1865 1867 kildonan gold rush 1869 black friday 1869 1870 gilded age 2nd industrial revolution 1870 1914 coromandel gold rushes c 1870 c 1890 cassiar gold rush c 1870 c 1890 long depression 1873 1879 panic of 1873 black hills gold rush 1874 1880 colorado silver boom 1879 1893 western australian gold rushes c 1880 c 1900 indiana gas boom c 1880 1903 ohio oil rush c 1880 c 1930 depression of 1882 1885 panic of 1884 cayoosh gold rush 1884 witwatersrand gold rush 1886 1887 88 recession baring crisis 1890 1891 cripple creek gold rush c 1890 c 1910 panic of 1893 1893 1897 australian banking crisis of 1893 black monday 1894 panic of 1896 klondike gold rush 1896 1899 second nova scotia gold rush 1896 1903 kobuk river stampede 1897 1899 mount baker gold rush 1897 c 1925 1899 1900 recession nome gold rush 1899 1909 fairbanks gold rush c 1900 c 1930 texas oil boom 1901 c 1950 panic of 1901 1902 1904 cobalt silver rush 1903 c 1930 panic of 1907 1907 1908 porcupine gold rush 1909 c 1960 panic of 1910 11 1910 1912 financial crisis of 1914 1913 14 world war home fronts interwar period 1914 1945 world war i economy and home fronts australia canada united kingdom united states post world war i recession 1918 1919 recession of 1920 1921 1920s florida land boom c 1920 1925 roaring twenties 1923 1924 recession 1926 1927 recession great depression 1929 1939 wall street crash of 1929 panic of 1930 great contraction 1929 1933 recession of 1937 1938 australia canada india south africa united kingdom united states 1930s kakamega gold rush third nova scotia gold rush 1932 1942 world war ii home front australia canada united kingdom united states post wwii expansion 1970s stagflation 1945 1982 great compression 1945 recession recession of 1949 1948 1949 hong kong and singapore asian tiger expansions 1950 1990 1951 canada recession recession of 1953 1953 1954 recession of 1958 1957 1958 recession of 1960 1961 kennedy slide of 1962 poseidon bubble 1969 1970 recession of 1969 1970 1970s commodities boom 1973 1975 recession 1973 1974 stock market crash secondary banking crisis of 1973 1975 1970s energy crisis 1973 1980 1973 oil crisis 1979 oil crisis steel crisis 1973 1982 1976 sterling crisis silver thursday 1980 early 1980s recession 1980 1982 united states computer age second gilded age 1982 present great moderation 1982 2007 1980s oil glut black saturday 1983 new zealand property bubble c 1985 savings and loan crisis 1986 1995 black monday 1987 friday the 13th mini crash 1989 early 1990s recession 1990 1991 australia united states 1990 oil price shock rhode island banking crisis 1990 1992 1991 indian economic crisis 1990s united states boom 1991 2001 1990s india economic boom hyperinflation in zimbabwe 1991 present black wednesday 1992 1994 bond market crisis 1994 papua new guinea financial crisis dot com bubble 1995 2004 stock market downturn of 2002 1997 asian financial crisis october 27 1997 mini crash early 2000s recession 2001 9 11 stock market crash 2000s commodities boom 2000 2014 united states housing bubble 2002 2006 canadian property bubble 2002 2003 myanmar banking crisis 2000s energy crisis 2003 2008 north dakota oil boom 2006 2015 uranium bubble of 2007 great recession 2007 2009 australia and new zealand bangladesh india malaysia pakistan and sri lanka british west indies canada south africa united kingdom united states 2008 financial crisis september october november december 2009 subprime mortgage crisis 2000s u s housing market correction u s bear market of 2007 2009 2007 2010 u s bank failures corporate debt bubble 2...