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

Answer 1

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 1^st,2^nd,3^rd and 4^th 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).