Question

You invested $4,500 in a project which gave you a return of 14.9% the 1st year. You were quite happy, but the 2nd year wasn't as good. You lost 6.8% that year. The 3rd year was better - you made 5.5% on this investment.   What was your annual average rate of return over the three years?

Answer 1

14.9% or 14.9/100 = +0.149 (gain)

6.8% or 6.8/100 = -0.068 (loss)

5.5% or 5.5/100 = +0.055 (gain)

first, we will add 1 to each annual return

this gives

1st year = 0.149+1 = 1.149 =R1

2nd year = -0.068+1 = 0.932 = R2

3rd year = 0.055+1 = 1.055 = R3

Now, we need to calculate the combined percent

here n is the number of years, which is n =3

setting the values, we get

= 1.04151

Now subtracting 1 from the above value and multiplying it with 100 to get the required annualized average rate of return

we get, 1.04151-1 = 0.04151

now, 100*0.04151 = 4.151%

So, required annual average rate of return over the three years is 4.151%