Suppose you buy a piece of property for $100, and the appreciated yearly values

Question

Suppose you buy a piece of property for $100, and the appreciated yearly values are given in the table below: End of Year 1: Value = $112.7 End of Year 2: Value = $144.4 End of Year 3: Value = $135.3 End of Year 4: Value = $192.4 Find the geometric mean rate of return (in terms of percentage) for this investment.
Plz step by step Suppose you buy a piece of property for $100, and the appreciated yearly values are given in the table below: End of Year 1: Value = $112.7 End of Year 2: Value = $144.4 End of Year 3: Value = $135.3 End of Year 4: Value = $192.4 Find the geometric mean rate of return (in terms of percentage) for this investment.
Plz step by step Suppose you buy a piece of property for $100, and the appreciated yearly values are given in the table below: End of Year 1: Value = $112.7 End of Year 2: Value = $144.4 End of Year 3: Value = $135.3 End of Year 4: Value = $192.4 Find the geometric mean rate of return (in terms of percentage) for this investment.
Plz step by step

Explanation / Answer

The formula for computing the geometric mean rate of return (g) is g = [(1+r1)(1+r2)(1+r3)(1+r4)]1/4 -1 where r1,r2,r3,r4 are the rates of return in the 1st,2nd,3rd and 4th years. Here, r1 = (112.7-100)/100 = 0.127, r2 = (144.4-112.7)/112.7 = 0.28123, r3 = (135.3-144.4)/144.4 =-0.06302, and r4 = (192.4-135.3)/135.3 =0.422025. Then g = [1.127*1.28123*0.93698*1.42205]1/4 -1 = (1.923960727)0.25 -1 = 1.177738984-1 = 0. 177738984 = 17.77 % ( on rounding off to 2 decimal places).

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