Question

The return on investment earned by atkins construction company for four successive years was 30% 20% -40% and 200%. What is the geometric mean rate of return on investment?

Answer 1

The geometric mean rate of return on investment is 29.45%

What is arithmetic mean rate of return?

Arithmetic rate of return is the sum of all returns divided by the number of periods for which the returns were indicated.

Arithmetic rate of return=sum of returns/number of returns

number of returns in this case is 4 since the returns were for 4 years

arithmetic rate of return=(30%+20%-40%+200%)/4

arithmetic rate of return=52.50%

What is geometric mean rate of return ?

It is the return computed using a different approach as shown by the formula below:

geometric mean rate of return= ((1 + R1) × (1 + R2) × ... × (1 +Rn))(1/n) - 1

R1=year 1 return=30%

R2=year 2 return=20%

R3=year 3 return=-40%

R4=year 4 return=200%

n=4(the returns for 4 years)

geometric mean rate of return=((1+30%)*(1+20%)*(1-40%)*(1+200%))^(1/4)-1

Remember the return in year 3 is negative 40%, using a positive return would lead a wrong conclusion

geometric mean rate of return=1.2945-1

geometric mean rate of return=29.45%

The geometric mean rate of return on investment is 29.45%

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