35 Suppose that the rate of return for a particular stock du

3.5 Suppose that the rate of return for a particular stock during the past two years was 10% for one of the years and 30% for the other year. Compute the geometric rate of return per year. (Note: A rate of return of 10% is recorded as 0.10. and a rate of return of 30% is recorded as 0.30.)

Solution

Let r = the geometric rate.

The amount accumulated, is P is the principal is

A = P(1 + 0.10)(1 + 0.30)

In terms of the geometric rate,

A = P(1 + r)^2

Thus,

P(1 + 0.10)(1+0.30) = P(1 + r)^2

(1 + 0.10)(1+0.30) = (1 + r)^2

1.43 = (1 + r)^2

1 + r = 1.195826074

r = 0.195826074 = 19.583% [ANSWER]