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Of the following four types of savings account plans, which option would yield e...


Question

Of the following four types of savings account plans, which option would yield exponential growth of the money in the account?

Options

A)
Each successive year, 2% of the initial savings is added to the value of the account.
B)
Each successive year, 1.5% of the initial savings and $100 is added to the value of the account.
C)
Each successive year, 1% of the current value is added to the value of the account.
D)
Each successive year, $100 is added to the value of the account.

The correct answer is C.

Explanation:

Choice C is correct. Linear growth is characterized by an increase of a quantity at a constant rate. Exponential growth is characterized by an increase of a quantity at a relative rate; that is, an increase by the same factor over equal increments of time. In choice C, the value of the account increases by 1% each year; that is, the value is multiplied by the same factor, 1.01, each year. Therefore, the value described in choice C grows exponentially.

Choices A and B are incorrect because the rate depends only on the initial value, and thus the value increases by the same amount each year. Both options A and B describe linear growth. Choice D is incorrect; it is also a description of linear growth, as the increase is constant each year.


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