Question

The graph below represents compound interest over time with an initial investment of $600 at in interest rate of 6% compounded annually. Which of these statements describes the situation?-it will take less than 10 years to double the initial investment-it will take less than 20 years to triple the initial investment-it will take more than 15 years to double the investment-it will take more than 30 years to triple the initial investment

Answer 1

It will take less than 20 years to triple the investment.

Step-by-step explanation

We want to identify the statement that best describes the situation represented by the graph of the compound interest over time.

To do this, let us find at what point the compound amount doubles and triples.

Since the initial investment is $600, it implies that double this investment is $1200, and triple this investment is $1800.

Hence, we have to identify what happens at these points on the graph.

Notice that when y approaches $1200 on the vertical axis, x is greater than 10 and less than 15. It occurs at about x = 12 years.

Also, notice that when y approaches $1800 on the vertical axis, x is less than 20 years (also less than 30 years). It occurs at about x = 19 years.

Hence, the only correct statement that describes the situation is that it will take less than 20 years to triple the investment.

The correct answer is the second option.