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:
[tex]M = \frac{100 + a}{100}[/tex]
In this problem, two increases of 5%, thus:
[tex]M = \frac{100 + 5}{100} = 1.05[/tex]
Another of x, that we want to find, and the result is a increase of 16%, thus:
[tex]M = \frac{100 + 16}{100} = 1.16[/tex]
The three increases(5%, 5% and x%) result in a increase of 16%, thus:
[tex]1.05(1.05)(x) = 1.16[/tex]
[tex]x = \frac{1.16}{(1.05)^2}[/tex]
[tex]x = 1.052[/tex]
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 https://brainly.com/question/21806362
