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Chapter 1: Problem 13

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

Expert verified
Jasmine has 30% of her portfolio invested in bonds.

Step by step solution

01

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 \( 2 \times 3x = 6x \).
02

Set Up the Equation

The total investment is \(100,000\): \( x \) (cash) + \( 3x \) (bonds) + \( 6x \) (stocks) = \( 100,000 \). The equation is: \( x + 3x + 6x = 100,000 \).
03

Simplify and Solve the Equation

Combine like terms in the equation: \( 10x = 100,000 \). To find \( x \), divide both sides by 10: \( x = 10,000 \).
04

Calculate the Amount Invested in Bonds

Since \( x \) is \( 10,000 \), the amount invested in bonds is \( 3x = 3 \times 10,000 = 30,000 \).
05

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: \( \frac{30,000}{100,000} \times 100\% = 30\% \).
06

Conclusion

Jasmine has 30% of her portfolio invested in bonds.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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鈥檚 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.

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Most popular questions from this chapter

A chef is making cookies from scratch. He requires a set period of time to gather the ingredients and to get everything set up to make the cookies. Then the chef needs a set period of time to make each individual cookie. If c represents the total number of cookies he is making and if t represents the total amount of time it takes to make \(c\) cookies, what is the meaning of the 20 in this equation: \(\mathrm{t}=20+10 \mathrm{c}\) ? (A) How much time it takes to make each individual cookie (B) The fixed cost of the cookie ingredients (C) The maximum number of cookies he can make in 10 minutes (D) The amount of time it takes him to set things up prior to making a cookie

(A) NO CHANGE (B) to go to Mars, however won't (C) to go to Mars but won't (D) to go to Mars, and, won't

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A professor will cancel his sociology class if the number of students in attendance is less than or equal to \(10 .\) Which of the following expressions would give the possible values of students, \(S\), necessary for the professor to conduct class, given that \(S\) is an integer? (A) \(S<10\) (B) \(S>10\) (C) \(\quad S \leq 10\) (D) \(\quad S \geq 10\)

A roller coaster requires riders to be at least 48 inches tall. Given that there are approximately \(2.54\) centimeters in an inch, how tall must a rider be to the nearest whole centimeter to ride the roller coaster? (A) 96 (B) 122 (C) 148 (D) 190
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