Question

Jasmine has \(\$ 100,000\) in an investment portfolio, divided among only three categories: stocks, bonds, and cash. She has twice as much invested in stocks as she does in bonds. She also has three times as much invested in bonds as she has in cash. What percent of Jasmine's portfolio is invested in bonds? A) \(22 \%\) B) \(27 \%\) C) \(30 \%\) D) \(44 \%\)

Short answer

Jasmine has 30% of her portfolio invested in bonds.

Step-by-step solution

Define the Variables

Let \( x \) represent the amount invested in cash. From the problem, we know that Jasmine has three times as much invested in bonds compared to cash, so the bonds amount is \( 3x \). Since the investment in stocks is twice the investment in bonds, it is \( 2 \times 3x = 6x \).

Set Up the Equation

The total investment is \(100,000\): \( x \) (cash) + \( 3x \) (bonds) + \( 6x \) (stocks) = \( 100,000 \). The equation is: \( x + 3x + 6x = 100,000 \).

Simplify and Solve the Equation

Combine like terms in the equation: \( 10x = 100,000 \). To find \( x \), divide both sides by 10: \( x = 10,000 \).

Calculate the Amount Invested in Bonds

Since \( x \) is \( 10,000 \), the amount invested in bonds is \( 3x = 3 \times 10,000 = 30,000 \).

Calculate the Percentage of the Bonds Investment

To find the percentage of bonds investment, divide the amount in bonds by the total portfolio value and multiply by 100: \( \frac{30,000}{100,000} \times 100\% = 30\% \).

Conclusion

Jasmine has 30% of her portfolio invested in bonds.

Key concepts

Investment Portfolio Math

Investment portfolio math involves organizing and calculating different amounts of money allocated in various investment categories. Picture an investment portfolio like a pie that is divided into different slices. Each slice represents a portion of the total investment allocated to a specific category, such as stocks, bonds, or cash.

Managing an investment portfolio effectively means understanding how each slice of the pie contributes to the entire portfolio. For Jasmine's situation, she needs to apportion her investments in stocks, bonds, and cash. This requires setting up a strategic plan and understanding the contribution of each type of investment.

• A balanced portfolio often involves proportional investments in different assets.
• Investment in stocks, bonds, and cash needs to be calculated accurately to draw meaningful insights.
• Understanding how to segregate funds helps in minimizing risk while aiming for returns.

Percentages in Investments

Percentages play a crucial role when analyzing and managing investments. In Jasmine's problem, understanding the percentage of her portfolio invested in each category reveals the structure of her investments.

When looking at percentages, they provide a way to see the proportion each investment type takes up of the entire portfolio. Knowing the percentage helps Jasmine assess risks and make informed decisions about her investments.

• The formula used is: \( \text{Percentage} = \frac{\text{Part}}{\text{Total}} \times 100\% \).
• Percentages facilitate comparisons even if the actual values are very different.
• For Jasmine, bonds account for \(30\%\) of her portfolio, giving her a piece of mind on where the largest part of her assets lie.

Algebraic Equations in Finance

Algebraic equations are powerful tools in financial calculations. They simplify complex investment situations into manageable calculations as seen in Jasmine's problem.

By defining variables, one converts real-world financial scenarios into equations that can be solved systematically. These equations help predict and decide necessary actions depending on different financial goals.

• Algebra helps describe how different investments relate to one another, such as Jasmine’s stocks being twice her bonds.
• The process involves setting up equations: Here, \( x + 3x + 6x = 100,000 \).
• Solving these equations allows investors to determine exact figures for each category, guiding better financial decisions.