You anticipate that a $2000 investment in a local business will pay an average of 4% interest in each of the next 5 years. Determine to the nearest dollar the amount of the investment at the end of 5 years.

Question

Mathematics

Manuel Brock

19 May, 17:04

You anticipate that a $2000 investment in a local business will pay an average of 4% interest in each of the next 5 years. Determine to the nearest dollar the amount of the investment at the end of 5 years.

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Maverick Ryan · Answer 1

Since this is a problem in exponential growth/decay, y = ab^x is the formula that will be used to solve this problem.

The initial value, "a", is the value you start out with and in this case, it is $2000.

The growth/decay factor is what "b" represents, and it is 4%. We need to change the percentage into a decimal, so we will take the percent symbol, change it into a decimal, and move it two places to the left. This is make it 0.04. The problem also mentions interest, implying an exponential growth. Therefore, you will add 0.04 by 1: 1+0.04 = 1.04.

The "x" represents an amount of time. It is 5 years. The equation should be written like this:

y = 2000 (1.04) ^5

y = 2433.30. When rounded to the nearest dollar, it is $2433.