Distribution and Statistics

Question

A two-year investment breaks even at the end of two years but yielded a 36% loss in the first year. Find the average annual rate of return for this investment.

____%

Any help is much appreciated.

Answer 1

Let's assume the investment at time 0 is notated as x.

During the first year the annual rate of return was -36%

At time 1, the investment is worth: x - 0.36x = 0.64x

During the second year the investment went from being 0.64x back to x.

Therefore the return for the second year is:

Value at time 2/value at time 1 = x/0.64x = 56.25%

Therefore, the average return over the 2 years is: (-0.36 + 0.5625)/2 = 10.125%