Question

Over an 8-year period, Katrina's $$\$ 14,000$$ investment in the stock market increased by \(180 \%\). What was the value of her investment at the end of that period? A. $$\$ 16,520$$ B. $$\$ 25,200$$ C. $$\$ 39,200$$ D. $$\$ 252,000$$

Short answer

The value of Katrina's investment at the end of the 8-year period was $$\$ 39,200$$.

Step-by-step solution

Calculate the percent increase in investment

To find the increase in investment, we will multiply the initial investment amount by the percent increase. The formula for this is: Increase in investment = (Initial investment × percent increase) / 100 Where, initial investment is $$\$ 14,000$$ and percent increase is \(180 \%\).

Calculate the increased amount

Now, we will plug in the values from the exercise into the formula: Increase in investment = (\(14,000 \times 180\)) / 100 Increase in investment = \(2,520,000 / 100\) Increase in investment = $$\$ 25,200$$

Calculate the final investment value

To find the final investment value, we simply add the initial investment amount and the increase in investment: Final investment value = Initial investment + Increase in investment Final investment value = $$\$ 14,000 + \$ 25,200$$ Final investment value = $$\$ 39,200$$ Now, let's look at the given options to see which matches our calculated final investment value: A. $$\$ 16,520$$ B. $$\$ 25,200$$ C. $$\$ 39,200$$ D. $$\$ 252,000$$ The correct option is: C. $$\$ 39,200$$

Key concepts

Stock Market Investment

Investing in the stock market offers significant opportunities for growing your wealth over time. When you invest, you're essentially buying shares of a company, making you a partial owner with the hope that the company's value will rise in the future. Stock market investments can be a powerful way to build wealth, as historically, stock markets tend to offer higher average returns compared to other investment types like bonds or savings accounts.

However, investing in the stock market also involves certain risks. The value of stocks can fluctuate, leading to potential gains, but also losses. It is important to take into account these risks and to diversify your investments, which means spreading your money across various companies and sectors. This reduces the risk of losing all your money if one company performs poorly.

• Stock market investments can provide higher returns but come with higher risks.
• Investing involves buying shares of companies, making you a partial owner.
• Diversification is crucial to reduce risk.

Considering these factors, individuals like Katrina can realize significant gains, such as her 180% increase in investment, when the stock market performs well.

Investment Growth

Investment growth refers to the increase in the value of an investment over time. This can be due to various factors such as an increase in the company's value, good management, or favorable economic conditions. Understanding how investments grow is key to maximizing returns and planning for future financial goals.

When an investment grows by a certain percentage over a specified period, this is often expressed in terms of percentage increase. For example, if you start with a $14,000 investment, and it grows by 180%, it means it has more than doubled in value. Calculating investment growth involves understanding percentage calculations and how they apply to the initial amount.

In Katrina's case, the investment growth calculation was straightforward. Her $14,000 turned into an additional $25,200 over 8 years, resulting in a final investment of $39,200. This growth is the result of the compounding effect, where the investment not only grows based on the initial amount but also on the profits previously earned:

• Investment growth reflects the increase in value over time.
• Growth can be due to various factors like good economic conditions or company performance.
• Calculations often express growth in percentage terms.

This highlights the importance of choosing investments wisely and being aware of market trends.

Basic Math Problem-Solving

Solving basic math problems is a valuable skill in everyday life, especially when dealing with financial decisions like investments. In problems like Katrina's investment scenario, the key is to break down the problem step by step.

A common formula used in calculating percentage increase or growth is:\[\text{Increase in Value} = \frac{\text{Initial Investment} \times \text{Percentage Increase}}{100}\]

This formula helps determine how much more the investment value is going to be relative to the original sum. Once you have this increase, it can be added back to the initial investment to find the total final value:

\[\text{Final Investment Value} = \text{Initial Investment} + \text{Increase in Value}\]

For those learning basic math problem-solving methods, practicing these problems can increase confidence in handling real-life situations involving percentages and financial calculations. Here are some helpful tips:

• Understand the problem and identify what is given and what needs to be found.
• Use the appropriate formulas and substitute the given values.
• Check your work to ensure the calculations are correct.

Mastering these techniques ensures you can tackle similar tasks with ease and accuracy.