Unit 6 Test: Investing Strategies & Exponential Functions

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25 questions

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Part 2: Maths Skills Open Response

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Library

Unit 6 Test: Investing Strategies & Exponential Functions

Last updated almost 3 years ago

25 questions

Note from the author:

Financial Algebra-NGPF

Instructions

Part 1:  Multiple Choice 

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Part 2: Maths Skills Open Response

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The data points represent a fund’s prices over time. Based on the exponential regression model…
a. Write the equation for the fund’s predicted price after x years. Round to the nearest hundredth.
b. Based on the model, predict the fund’s approximate price after 6 years. Show your work or explain your reasoning.

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Is this model a good fit for the data? Why or why not?

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Antonina goes on Wheel of Fortune and wins $12,000 after taxes. She decides that she will invest this money with the goal of putting a $20,400 down payment on a house. She puts the money in a mutual fund that has had a historical return of 7.5%.
a. Write an exponential equation that represents Antonina’s investment where x represents years and f(x) represents her investment after x years. Assume the mutual fund earns a 7.5 annual rate of return.
b. Calculate how long it will take to reach her investment goal. Round to 2 decimal places.

Financial Algebra-NGPF

Part 1:  Multiple Choice 

The S&P 500 is…

An actively managed mutual fund

A diverse collection of stocks and bonds

An index of the  500 largest publicly-traded companies in the world

An index of the 500 largest publicly-traded companies in the US

All of the following are true about robo-advisors, EXCEPT…

Robo-advisors use an algorithm to automate the investing process

Robo-advisors generally have lower fees than a traditional financial advisor

Robo-advisors generally invest your portfolio based on your goals and risk tolerance

Robo-advisors generally have a higher account minimum than a traditional financial advisor

Alberto has decided to invest his retirement money into a mutual fund filled with mid-sized US companies. The fund manager is…

The budgeting software Alberto uses to make sure he has enough saved every month

The person who selects which stocks to include in the fund

A CEO at one of those midsize companies

The website where Alberto logs in to check his fund’s value

All of the following are factors to consider when opening a brokerage account EXCEPT

Who will manage the account

The location of the brokerage company

Your investing goals

Fees that will be charged

Alma recently started investing in a target-date fund with a planned retirement date that is 38 years in the future. How is the portfolio in her TDF most likely allocated?

Half stocks and half bonds

Her TDF allocation will depend on the specific securities she selects

Majority stocks and a small percentage of bonds

Majority bonds and a small percentage of stocks

Which fund will most working American citizens have access to at retirement?

A Roth IRA

A traditional IRA

A pension plan

Social Security

If you invest money into an index fund that tracks the Dow Jones Industrial Average, you would expect…

A lot of high fees, because there are only 30 companies in that index

Your fund manager to contact you on a regular basis with suggestions on whether to buy or sell

To outperform most other investors because of the elite status of this index

Your returns to track the performance of 30 large US companies

Which statement about the investment fees associated with mutual funds is true?

Fees are typically set at 10 to 15%, annually, of the amount you have invested

You’ll only pay fees to your fund manager if your portfolio has a return over 5%

You’ll pay a one-time fee when you start your investment portfolio with a mutual fund

Fees, compounded over the life of your investment, can substantially decrease your returns

Which type of fund is usually passively managed, can be traded throughout the day, and is bought directly from other investors like a stock?

Target date fund

Exchange-traded fund

Robo-advisor

Mutual fund

In 2022, Noah decided to start investing in a target-date fund at Alpine brokerage. They are 24 years old, have been working for 5 years, and are planning on retiring at 67. Which target-date fund should they choose?

Alpine Target Retirement 2060 Fund

Alpine Target Retirement 2065 Fund

Alpine Target Retirement 2070 Fund

Alpine Target Retirement 2075 Fund

Zora has $5,000 to invest. When assessing her goals, she decides that she wants to create a low-risk, low-volatility portfolio. Based on this assessment, a good strategy for Zora would be:

Lump Sum Investing

Average Paycheck Investing

After Tax Averaging

Dollar-Cost Averaging

Ash remembers learning about both 401(k)s and IRAs in his personal finance class during high school. He’s early in his career, and he can really only afford to fund one type of account with about $100 per month right now. What should he do?

Fund a savings account, because it will guarantee an interest rate, rather than leaving his retirement up to a risky investment option

Fund a traditional IRA, because it will offer him, by far, the best tax advantages

Fund a 401(k) because his employer is offering a match, up to 3% of his salary

Fund neither account, because $100 does not meet the minimum requirements for any retirement account type

Which of the following is an example of the bias of Chasing Trends?

Researching the long term growth strategy of a company

Buying cryptocurrency because you saw a headline about it reaching its highest price ever

Buying a stock when it has hit its lowest price of the year

Buying stock in an industry that is not represented in your portfolio to increase diversity

Each of the following factors impacts how much money you will have available at retirement EXCEPT…

How old you are when you start investing

Whether you qualify for Social Security benefits

What percent of your income you invest each month

How often you log into your online brokerage account

Kendall completed her med school training 10 years ago and is now a successful highly-paid surgeon at a major hospital. What type of account would be most beneficial for Kendall to use to start saving for retirement, so she can enjoy time off after a stressful career?

A Roth IRA, because she can pay taxes on the money now and take it out tax-free later

A regular brokerage account, because tax advantages don’t matter that much

Social Security, because she will pay into it throughout her career

A traditional 401(k), because it will reduce her taxable income now

Evaluate:

3

4

10

27

Look at the graph. Which of the four functions has the smallest value for b?

Function a

Function b

Function c

Function d

Which of these functions has an asymptote at y = 2?

The assets managed by index funds have grown by approximately 14.91% per year

The model is not a good fit for the data points because the r2 value is close to 1

A linear regression model would likely have a higher r2 value

 

The model predicts that US index funds will manage approximately $1.7 trillion in assets in 2023

x=2

x=3

x=4

x=5

The data points represent a fund’s prices over time. Based on the exponential regression model…
a. Write the equation for the fund’s predicted price after x years. Round to the nearest hundredth.
b. Based on the model, predict the fund’s approximate price after 6 years. Show your work or explain your reasoning.

Is this model a good fit for the data? Why or why not?

Antonina goes on Wheel of Fortune and wins $12,000 after taxes. She decides that she will invest this money with the goal of putting a $20,400 down payment on a house. She puts the money in a mutual fund that has had a historical return of 7.5%.
a. Write an exponential equation that represents Antonina’s investment where x represents years and f(x) represents her investment after x years. Assume the mutual fund earns a 7.5 annual rate of return.
b. Calculate how long it will take to reach her investment goal. Round to 2 decimal places.

The S&P 500 is…

An actively managed mutual fund

A diverse collection of stocks and bonds

An index of the  500 largest publicly-traded companies in the world

An index of the 500 largest publicly-traded companies in the US

All of the following are true about robo-advisors, EXCEPT…

Robo-advisors use an algorithm to automate the investing process

Robo-advisors generally have lower fees than a traditional financial advisor

Robo-advisors generally invest your portfolio based on your goals and risk tolerance

Robo-advisors generally have a higher account minimum than a traditional financial advisor

Alberto has decided to invest his retirement money into a mutual fund filled with mid-sized US companies. The fund manager is…

The budgeting software Alberto uses to make sure he has enough saved every month

The person who selects which stocks to include in the fund

A CEO at one of those midsize companies

The website where Alberto logs in to check his fund’s value

All of the following are factors to consider when opening a brokerage account EXCEPT

Who will manage the account

The location of the brokerage company

Your investing goals

Fees that will be charged

Alma recently started investing in a target-date fund with a planned retirement date that is 38 years in the future. How is the portfolio in her TDF most likely allocated?

Half stocks and half bonds

Her TDF allocation will depend on the specific securities she selects

Majority stocks and a small percentage of bonds

Majority bonds and a small percentage of stocks

Which fund will most working American citizens have access to at retirement?

A Roth IRA

A traditional IRA

A pension plan

Social Security

If you invest money into an index fund that tracks the Dow Jones Industrial Average, you would expect…

A lot of high fees, because there are only 30 companies in that index

Your fund manager to contact you on a regular basis with suggestions on whether to buy or sell

To outperform most other investors because of the elite status of this index

Your returns to track the performance of 30 large US companies

Which statement about the investment fees associated with mutual funds is true?

Fees are typically set at 10 to 15%, annually, of the amount you have invested

You’ll only pay fees to your fund manager if your portfolio has a return over 5%

You’ll pay a one-time fee when you start your investment portfolio with a mutual fund

Fees, compounded over the life of your investment, can substantially decrease your returns

Which type of fund is usually passively managed, can be traded throughout the day, and is bought directly from other investors like a stock?

Target date fund

Exchange-traded fund

Robo-advisor

Mutual fund

In 2022, Noah decided to start investing in a target-date fund at Alpine brokerage. They are 24 years old, have been working for 5 years, and are planning on retiring at 67. Which target-date fund should they choose?

Alpine Target Retirement 2060 Fund

Alpine Target Retirement 2065 Fund

Alpine Target Retirement 2070 Fund

Alpine Target Retirement 2075 Fund

Zora has $5,000 to invest.  When assessing her goals, she decides that she wants to create a low-risk, low-volatility portfolio.  Based on this assessment, a good strategy for Zora would be:

Lump Sum Investing

Average Paycheck Investing

After Tax Averaging

Dollar-Cost Averaging

Ash remembers learning about both 401(k)s and IRAs in his personal finance class during high school. He’s early in his career, and he can really only afford to fund one type of account with about $100 per month right now. What should he do?

Fund a savings account, because it will guarantee an interest rate, rather than leaving his retirement up to a risky investment option

Fund a traditional IRA, because it will offer him, by far, the best tax advantages

Fund a 401(k) because his employer is offering a match, up to 3% of his salary

Fund neither account, because $100 does not meet the minimum requirements for any retirement account type

Which of the following is an example of the bias of Chasing Trends?

Researching the long term growth strategy of a company

Buying cryptocurrency because you saw a headline about it reaching its highest price ever

Buying a stock when it has hit its lowest price of the year

Buying stock in an industry that is not represented in your portfolio to increase diversity

Each of the following factors impacts how much money you will have available at retirement EXCEPT…

How old you are when you start investing

Whether you qualify for Social Security benefits

What percent of your income you invest each month

How often you log into your online brokerage account

Kendall completed her med school training 10 years ago and is now a successful highly-paid surgeon at a major hospital. What type of account would be most beneficial for Kendall to use to start saving for retirement, so she can enjoy time off after a stressful career?

A Roth IRA, because she can pay taxes on the money now and take it out tax-free later

A regular brokerage account, because tax advantages don’t matter that much

Social Security, because she will pay into it throughout her career

A traditional 401(k), because it will reduce her taxable income now

Evaluate:  

3

4

10

27

Look at the graph. Which of the four functions has the smallest value for b?

Function a

Function b

Function c

Function d

Which of these functions has an asymptote at y = 2?

The assets managed by index funds have grown by approximately 14.91% per year

The model is not a good fit for the data points because the r2 value is close to 1

A linear regression model would likely have a higher r2 value

 

The model predicts that US index funds will manage approximately $1.7 trillion in assets in 2023

x=2

x=3

x=4

x=5