Using the returns for the years 1926–1931 from Table 6‐1, determine the geometric mean for this period. Show how the same result can be obtained from the ending wealth index value for 1931 of 0.7405.

Table 6‐1

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TABLE 6-1 Historical Composite Stock Price Index, Based on Standard & Poor's 500 Index, Dividends in Index Form, and Returns (Rs), 1926-2014. Values are End of Year Year 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983. 1984 1985 1986 1987 1988 1989 1990 1991 Index Value 13.49 17.66 24.35 21.45 15.34 8.12 6.89 10.1 9.5 13.43 17.18 10.55 13.21 12.49 10.58 8.69 9.77 11.67 13.28 17.36 15.3 103.86 92.06 92.15 102.09 118.05 97.55 68.56 90.19 107.46 95.1 96.11 107.94 135.76 122.55 140.64 164.93 167.24 211.28 242.17 247.08 277.72 353.4 330.22 417.09 Dividend 0.69 0.77 0.85 0.97 0.98 0.82 0.50 0.44 0.45 0.47 0.72 0.80 0.51 0.62 0.67 0.71 0.59 0.61 0.64 0.66 0.71 3.07 3.16 3.14 3.07 3.15 3.38 3.60 3.68 4.05 4.67 5.07 5.65 6.16 6.63 6.87 7.09 7.53 7.90 8.28 8.81 9.73 11.05 12.10 12.20 Return (%) 13.80 36.62 42.70 -7.93 -23.92 -41.72 -8.99 52.98 -1.49 46.32 33.28 -33.93 30.05 -0.76 -9.93 -11.15 19.22 25.69 19.28 35.69 -7.78 10.84 -8.32 3.51 14.12 18.72 -14.50 -26.03 36.92 23.64 -7.16 6.39 18.19 31.48 -4.85 20.37 22.31 5.97 31.06 18.54 5.67 16.34 31.23 -3.14 30.00 Year 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1992 1993. 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Index Value 15.3 15.2 16.76 20.41 23.77 26.57 24.81 35.98 45.48 46.67 39.99 55.21 59.89 58.11 71.55 63.1 75.02 84.75 92.43 80.33 96.47 435.71 466.45 459.27 615.93 740.74 970.43 1229.23 1469.25 1320.28 1148.08 879.82 1111.92 1211.92 1248.29 1418.3 1468.36 903.25 1115.1 1257.64 1257.6 1426.19 1848.36 2058.9 Dividend 0.84 0.93 1.14 1.47 1.41 1.41 1.45 1.54 1.64 1.74 1.79 1.75 1.83 1.95 2.02 2.13 2.28 2.50 2.72 2.87 2.92 12.38 12.58 13.18 13.79 14.90 15.50 16.20 16.48 16.27 15.74 16.07 17.39 19.44 22.22 24.88 27.73 28.39 22.41 22.73 26.43 31.25 34.99 39.44 Return (%) 5.49 5.42 17.76 30.55 23.37 17.71 -1.17 51.23 30.96 6.44 -10.48 42.44 11.79 0.28 26.60 -8.83 22.50 16.30 12.27 -9.99 23.73 7.43 9.94 1.29 37.11 22.68 33.10 28.34 20.87 -9.03 -11.85 -21.97 28.36 10.74 4.83 15.61 5.48 -36.55 25.94 14.82 2.10 15.89 32.05 13.52