6.6.0: Exercises
- Page ID
- 171718
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Which account has the greatest flexibility, savings, certificate of deposit, or money market?
Why are interest rates on savings accounts, CDs, and money market accounts low?
Which of savings accounts, certificates of deposit, and money market accounts, allow for transactions?
How does number of years impact the return on investment?
In the following exercises, find the future value of the account based on the information given.
The amount of $3,000 deposited in a CD bearing 2.6% compounded semi-annually for 3 years.
The amount of $1,500 deposited in a money market account bearing 3.11% interest compounded monthly for 10 years.
The amount of $8,450 deposited in a savings account bearing 1.75% interest compounded monthly for 2 years.
The amount of $10,500 deposited in a savings account bearing 1.35% interest compounded quarterly for 20 years.
The amount of $24,800 deposited in a money market account bearing 2.53% interest compounded semi-annually for 13 years.
The amount of $16,400 deposited in a CD bearing 2.55% interest compounded quarterly for 18 years.
In the following exercises, find the return on investment based on the specified exercise. Round to two decimal places.
Account from Exercise 5.
Account from Exercise 6.
Account from Exercise 7.
Account from Exercise 8.
In the following exercises, find the future value of the ordinary annuities based on the payment, interest rate, compounding periods and length of time given.
The amount of $150 deposited monthly in an account bearing 4.22% interest compounded monthly for 20 years.
The amount of $500 deposited semi-annually in an account bearing 3.62% interest compounded semi-annually for 30 years.
The amount of $250 deposited quarterly in an account bearing 3.61% interest compounded quarterly for 25 years.
The amount of $250 deposited monthly in an account bearing 3.09% interest compounded monthly for 40 years.
The amount of $1,500 deposited annually in an account bearing 3.34% interest compounded annually for 10 years.
The amount of $1400 deposited semi-annually in an account bearing 2.78% interest compounded semi-annually for 30 years.
In the following exercises, find the payment per period necessary to reach a specified future value based on the given interest rate, compounding periods per year, and number of years. Recall, the number of payments per year and the number of compounding periods per year are the same.
Future value of $1,000,000 from an account bearing 3.94% interest compounded monthly for 40 years.
Future value of $500,000 from an account bearing 2.11% interest compounded quarterly for 30 years.
Future value of $750,000 from an account bearing 3.27% interest compounded monthly for 25 years.
Future value of $300,000 from an account bearing 3.59% interest compounded semiannually for 35 years.
Future value of $1,000,000 from an account bearing 3.62% interest compounded annually for 25 years.
Future value of $600,000 from an account bearing 4.02% interest compounded quarterly for 30 years.
Dina deposits $3,000 in a 5-year CD that bears 3.25% interest compounded quarterly. What is the CD worth after those 5 years?
Timothy deposits $1,200 in a savings account that bears 1.85% interest compounded monthly. If Timothy does not deposit or withdraw money from the account how much is in Timothy’s account after 3 years?
Leslie deposits $13,000 in a money market account that bears 2.55% interest compounded semi-annually. If Leslie does not withdraw or deposit money into the account, how much is in Leslie’s account after 6 years?
Jennifer deposits $8,500 in a 3-year CD bearing 2.71% interest compounded annually. How much is Jennifer’s CD worth after those 3 years?
Yasmin has analyzed her budget and decides to deposit $425 per month in an account bearing 3.99% interest compounded monthly. How much will be in the account after 20 years? After 30 years? After 40 years?
Ashliegh wants to save for an early retirement. She thinks she needs $1,250,000 to retire at the age of 55, which is 30 years from now. How much must she deposit per month in an account bearing 3.48% interest compounded monthly to reach her goal?
Colin plans out the next 38 years of his life. In order to retire in 38 years (age 65) with $1,450,000, how much should he deposit quarterly in an account bearing 4.21% interest compounded quarterly to reach his goal?
In the following exercises, different savings strategies will be compared.
Sam decides instead to delay investing in the account until her 35th birthday. How much will be in the account at age 65 (30 years)?
Sam decides to deposit the $300 per month until she turns 35 years old (11 years). She will then stop investing the $300 monthly, and just allow the money to earn interest until her 65th birthday (30 more years). How much will be in her account on her 65th birthday? Hint: First, compute the FV of the deposits. Then use that FV as the principal for a single deposit into an account bearing 3.75% interest compounded monthly.
Compare the results of the three investment strategies.
In the following exercises, different savings strategies will be compared.
Dahlia decides instead to delay investing in the account until her 34th birthday. How much will be in the account on her 68th birthday (34 years)?
Dahlia decides to deposit the $250 per month until her 34th birthday (11 years). She will then stop investing the $250 monthly, and just allow the money to earn interest until her 68th birthday (34 more years). How much will be in her account on her 65th birthday? Hint: First compute the \(FV\) of the deposits. Then use that \(FV\) as the principal for a single deposit into an account bearing 6.2% interest compounded monthly.
Compare the results of the three investment strategies.