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Daniel [21]
2 years ago
14

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

​
Mathematics
1 answer:
murzikaleks [220]2 years ago
5 0

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 <u>decimal multiplier</u> 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

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