6.7.0: Exercises
- Page ID
- 171719
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)What is the maturity date for a bond?
What is the issue price for a bond?
Stock investments increase in value in what two ways?
Which is the least risky of stocks, bonds, mutual funds, CDs?
Which type of individual retirement account allows pre-tax deposits?
What are the limits on contributions to individual retirement accounts in 2022?
Of bonds, stocks, mutual funds, CDs, and money market accounts, which do not allow for withdrawal until a certain time period has passed?
Which type of IRA allows the account to grow tax free, provided no withdrawals are made until after the age of \(59\frac{1}{2}\)?
Which of bonds, mutual funds, and CDs are professionally managed?
Why do mutual funds and IRAs have relatively low risk?
For the bonds with the given properties, find a. the amount paid each year and b. the total amount earned with the bond.
Issue price of $10,000 pays 3.5% annually, matures in 5 years.
Issue price of $3,400 pays 2.75% annually, matures in 10 years.
Issue price of $1,000 pays 2.8% annually, matures in 5 years.
Issue price of $5,000 pays 3.75% annually, matures in 15 years.
In the following exercises, find: a. the return on investment and b. the annual return for the bond described. Round to two decimal places.
Issue price of $10,000 pays 3.5% annually, matures in 5 years.
Issue price of $3,400 pays 2.75% annually, matures in 10 years.
Issue price of $1,000 pays 2.8% annually, matures in 5 years.
Issue price of $5,000 pays 3.75% annually, matures in 15 years.
40 shares of stock are owned. The dividend per share is $0.38 for a quarter. How much was earned in dividends on this stock this quarter?
150 shares of stock are owned. The dividend per share is $0.78 for a quarter. How much was earned in dividends on this stock this quarter?
100 shares of stock are owned. The dividend per share is $0.18 for a quarter. How much was earned in dividends on this stock this quarter?
250 shares of stock are owned. The dividend per share is $0.41 for a quarter. How much was earned in dividends on this stock this quarter?
For the following exercises, 70 shares of stock were purchased for $31.50 per share 5 years ago. Over the 5 years, the total of all dividends earned from this stock was $6.34 per share. The stock is sold for $34.83.
How much was earned with dividends and share price increase combined?
What was the return on investment for these stocks?
What was the annual return for these stocks?
For the following exercises, 10 shares of stock were purchased for $18.91 per share 3 years ago. Over the 3 years, the total of all dividends earned from this stock was $3.18 per share. The stock is sold for $22.01.
How much was earned with dividends and share price increase combined?
What was the return on investment for these stocks?
What was the annual return for these stocks?
For the following exercises, use the given stock table to answer the following:
- What was the 52-week low?
- What was the dividend?
- What is its year-to-date performance?
- What is its yield?
Stock table (data source: marketwatch.com)
In the following exercises, find the future value of the mutual fund or IRA with the given annual deposit, the duration of the investment, and the assumed annual, compounded, percentage rate.
IRA, annual deposit = $6,000, 25 years, assumed percentage rate of 11.3%
IRA, annual deposit = $4,800, 15 years, assumed percentage rate of 9.7%
Mutual fund, annual deposit = $7,500, 35 years, assumed percentage rate of 10%
Mutual find, annual deposit = $12,000, 40 years, assumed percentage rate of 9%
In the following exercises, find the annual deposit necessary, into an IRA or mutual fund, to reach the stated financial goal, given the assumed annual, compounded, interest rate, and the duration of the deposits. Convert that annual deposit to a monthly amount.
Mutual fund, goal = $1,000,000, 25 years, assumed percentage rate of 11.3%
Mutual fund, goal = $100,000, 15 years, assumed percentage rate of 9.7%
IRA, goal = $750,000, 35 years, assumed percentage rate of 10%
IRA, goal = $1,750,000, 40 years, assumed percentage rate of 9%
Francis’s employer matches 401(k) contributions up to 7% of annual salary. She makes $98,500. What is the maximum amount that the company will match for Francis?
Miles’ employer matches 401(k) contributions up to 4% of annual salary. He makes $38,500. What is the maximum amount that the company will match for Miles?
Ila’s employer matches 401(k) contributions, up to 4% of salary. She makes $49,000. She wants to deposit $3,000 of her own earnings per year ($250 per month). How much, including her employer’s matching funds, will be deposited into Ila’s account each year?
Georgia works at a company that matches 401(k) contributions up to 5.5% of salary. Georgia wants to deposit $6,000 of her own earnings per year ($500 per month) in her 401(k). If she makes $65,000 annually, how much, including employer contributions, will be deposited in Georgia’s account annually?
In the following exercises, Cheryl’s company offers a 401(k) account to all employees. The company will match employee contributions up to 6% of the employee’s salary. She earns $81,000 per year. Cheryl decides to deposit, or contribute, $10,000 annually in the 401(k). She expects a return of 9.5% per year.
How much will the company match?
What is her total contribution per year?
If she deposits into the account for 25 years, how much will her 401(k) be worth?
In the following exercises, Lavanya’s company offers a 401(k) account to all employees. Her annual salary is $58,000. The company will match employee contributions up to 7% of the employee’s salary. Lavanya decides to deposit $3,200 annually in the 401(k). She expects a return of 8.5% per year.
How much will the company match?
What is her total contribution per year?
If she deposits into the account for 20 years, how much will her 401(k) be worth?
In the following exercises, Ruslana wants to use her 401(k) to save $1,400,000 when she retires in 36 years. She assumes the plan will yield 11% compounded annually. Her company will match contributions up to 5% of annual salary. Her salary is $48,000.
How much total will need to be added to her account each year to reach her goal?
What is 5% of Ruslana’s salary?
The company will match up to 5% of Ruslana’s salary, which means half the payment (up to 5% of salary) will be contributed by the company. How much is half the necessary payment?
Does the answer to Exercise 51 exceed the result from Exercise 50?
If the answer to Exercise 52 is no, then the company contributes half the deposit in the 401(k). How much will the company contribute annually to the 401(k) if this is the case?
If the answer to Exercise 52 is yes, then the company contributes only the 5% match of Ruslana's salary. In this case, how much does the company contribute?
How much will Ruslana need to contribute per year, after the employer contribution?
Divide the answer to Exercise 55 by 12 to find the monthly contribution Ruslana will make.
In the following exercises, Remy wants to use his 401(k) to save $1,750,000 when he retires in 30 years. He assumes the plan will yield 10.4% compounded annually. His company will match contributions up to 6% of annual salary. His salary is $78,000.
How much total will need to be added to his account each year to reach his goal?
What is 6% of Remy’s salary?
The company will match up to 6% of Remy’s salary, which means half the payment (up to 6% of salary) will be contributed by the company. How much is half the necessary payment?
Does the answer to Exercise 59 exceed the result from Exercise 58?
If the answer to Exercise 60 is no, then the company contributes half the deposit in the 401(k). How much will the company contribute annually to the 401(k) if this is the case?
If the answer to Exercise 60 is yes, then the company contributes only the 6% of Remy’s salary. In this case, how much does the company contribute?
How much will Remy need to contribute per year, after the employer contribution?
Divide the answer to Exercise 63 by 12 to find the monthly contribution Remy will make.