Question

After two consecutive years of 5% rates of return, what rate of return in the third year will produce a cumulative gain of 16%? ​

Answer 1

Using decimal multipliers, it is found that a rate of return of 5.2% in the third year will produce a cumulative gain of 16%.

The decimal multiplier for a increase of a% is given by:

$M = \frac{100 + a}{100}$

In this problem, two increases of 5%, thus:

$M = \frac{100 + 5}{100} = 1.05$

Another of x, that we want to find, and the result is a increase of 16%, thus:

$M = \frac{100 + 16}{100} = 1.16$

The three increases(5%, 5% and x%) result in a increase of 16%, thus:

$1.05(1.05)(x) = 1.16$

$x = \frac{1.16}{(1.05)^2}$

$x = 1.052$

1.052 - 1 = 0.052

A rate of return of 5.2% in the third year will produce a cumulative gain of 16%.

A similar problem is given at brainly.com/question/21806362