Question

n the first two years your investment increases by 2.5% annually, in the third year it returns 12% but in the fourth year it goes down 7%. The "average rate of return" is determined using the geometric mean. What is the average annual rate of return over the four years

Answer 1

Answer:

Ans. The average annual rate of return over the four years is 2.792%

Explanation:

Hi, first let´s introduce the formula to use

$r(Average)=\sqrt[n]{(1+r(1))*(1+r(2))*(1+r(3))+...(1+r(n))}-1$

Where:

r(1),(2),(3)...n are the returns in each period of time

n =number of returns to average (in our case, n=4).

With that in mind, let´s find the average annual return over this four years.

$r(Average)=\sqrt[4]{(1+0.025)*(1+0.025)*(1+0.12)+(1-0.07))} -1=0.022792$

Therefore, the average annual return of this invesment in 4 years is 2.2792%

Best of luck.