You have two options for investing $500. The first earns 7% interest compounded annually, and
the second earns 7% simple interest. The figure shows the growth of each investment over a 30-
year period.
a. Determine which graph represents each type of investment. Explain your reasoning.
b. Which option would you choose? Explain
c. Just based on the information provided by the graph (without any calculation), can you estimate
the amount of money in your 7% interest compounded annually account after 45 years? Explain
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a. The graph that represents the 7% interest compounded annually would be the one that shows exponential growth over time, as compound interest grows faster than simple interest. The graph that represents 7% simple interest would show linear growth, as the amount earned each year is constant.
b. I would choose the investment with 7% interest compounded annually because it will result in a higher return on investment over time due to the compounding effect. As shown in the graph, the compounded interest investment grows exponentially, resulting in significantly more money after 30 years compared to the simple interest investment.
c. Based on the exponential growth shown in the graph for the 7% interest compounded annually investment, I can estimate that after 45 years, the amount of money in the account would be significantly higher compared to the initial $500 investment. The exponential growth curve suggests that the account balance would continue to grow at an increasing rate, resulting in a substantial amount of money after 45 years.
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