Complete
the following end-of-chapter exercises and problems from Chapter 5 of Foundations
of Finance. Write approximately 900 words for all of the answers combined.
**** Not really sure
how they expect just 900 words, I could be wrong.**** (side note from)
Study Problems 5-1,
5-4, 5-6, 5-11, 5-14, 5-19, 5-21, 5-31, 5-40, 5-41, and 5-50.
5-1.(Compound interest)
To what amount will the following investments accumulate?
a. $5,000 invested for 10 years at 10 percent compounded annually
b. $8,000 invested for 7 years at 8 percent compounded annually
c. $775 invested for 12 years at 12 percent compounded annually
d. $21,000 invested for 5 years at 5 percent compounded annually
5-2.(Compound value solving for
n) How many years will the following
take?
5-4.(Present value) What is
the present value of the following future amounts?
a. $800 to be received 10 years from now discounted back to the
present at 10 percent
b. $300 to be received 5 years from now discounted back to the
present at 5 percent
c. $1,000 to be received 8 years from now discounted back to the
present at 3 percent
d. $1,000
to be received 8 years from now discounted back to the present at 20 percent
5-6.(Present value of an annuity)
What is the present value of the following annuities?
a. $2,500 a year for 10 years discounted back to the present at 7
percent
b. $70 a year for 3 years discounted back to the present at 3
percent
c. $280 a year for 7 years discounted back to the present at 6
percent
d. $500 a
year for 10 years discounted back to the present at 10 percent
5-11.(Future value) Sales of
a new finance book were 15,000 copies this year and were expected to
increase by 20 percent per year. What are expected sales during
each of the next 3 years? Graph this
sales trend
and explain.
5-14.(Solving for PMT of an annuity) To pay for your child’s education, you wish to have accumulated
$15,000 at the end of 15 years. To do this you plan on depositing
an equal amount into the
bank at the end of each year. If the bank is willing to pay 6
percent compounded annually, how much
must you
deposit each year to reach your goal?
5-21.(Perpetuities) What is
the present value of the following?
a. A $300 perpetuity discounted back to the present at 8 percent
b. A $1,000 perpetuity discounted back to the present at 12
percent
c. A $100 perpetuity discounted back to the present at 9 percent
d. A $95
perpetuity discounted back to the present at 5 percent
5-31.(Comprehensive present value)
You are trying to plan for retirement in 10 years, and currently
you have $100,000 in a savings account and $300,000 in stocks. In
addition you plan on adding to
your savings by depositing $10,000 per year in your savings
account at the end of each of the next
5 years and then $20,000 per year at the end of each year for the
final 5 years until retirement.
a. Assuming your savings account returns 7 percent compounded
annually, and your investment
in stocks will return 12 percent compounded annually, how much
will you have at the
end of 10 years? (Ignore taxes.)
b. If you expect to live for 20 years after you retire, and at
retirement you deposit all of your
savings in a bank account paying 10 percent, how much can you
withdraw each year after
retirement (20 equal withdrawals beginning 1 year after you
retire) to end up with a zero
balance
upon your death?
5-40.(Future and present value using a calculator) Over the past few years Microsoft founder Bill
Gates’s net worth has fluctuated between $20 billion and $130
billion. In 2010 Gates was worth
about $28 billion after he reduced his stake in Microsoft from 21
percent to around 14 percent by
moving billions into his charitable foundation. Let’s see what
Bill Gates can do with his money in
the following problems.
a. I’ll take Manhattan? Manhattan’s native tribe sold Manhattan
Island to Peter Minuit for $24
in 1626. Now, 384 years later in 2010, Bill Gates wants to buy the
island from the “current
natives.” How much would Bill have to pay for Manhattan if the
“current natives” want a
6 percent annual return on the original $24 purchase price? Could
he afford it?
b. (Nonannual compounding using
a calculator) How much would Bill have
to pay for Manhattan
if the “current natives” want a 6% return compounded monthly on
the original $24 purchase
price?
c. Microsoft Seattle? Bill Gates decides to pass on Manhattan and
instead plans to buy the city
of Seattle, Washington, for $60 billion in 10 years. How much
would Mr. Gates have to invest
today at 10 percent compounded annually in order to purchase
Seattle in 10 years?
d. Now assume Bill Gates wants to invest only about half his net
worth today, $14 billion, in
order to buy Seattle for $60 billion in 10 years. What annual rate
of return would he have
to earn in order to complete his purchase in 10 years?
e. Margaritaville? Instead of buying and running large cities,
Bill Gates is considering quitting
the rigors of the business world and retiring to work on his golf
game. To fund his retirement,
Bill Gates would invest his $28 billion fortune in safe
investments with an expected
annual rate of return of 7 percent. Also, Mr. Gates wants to make
40 equal annual withdrawals
from this retirement fund beginning a year from today. How much
can Mr. Gates’s
annual
withdrawal be in this case?
5-41.(Compounding using a calculator) Bart Simpson, age 10, wants to be able to buy a really cool
new car when he turns 16. His really cool car costs $15,000 today,
and its cost is expected to increase
3 percent annually. Bart wants to make one deposit today (he can
sell his mint-condition original
Nuclear Boycomic book)
into an account paying 7.5 percent annually in order to buy his car in
6 years. How much will Bart’s car cost, and how much does Bart
have to save today in order to buy
this car at
age 16?
5-50.(Nonannual compounding using a calculator) Should we have bet the kids’ college fund at the dog
track? In the downturn of 2008–2009 investors suffered substantial
declines on tax-sheltered college
savings plans (called 529 plans) around the country. Let’s look at
one specific case of a college
professor (let’s call him Prof. ME) with two young children. Two
years ago Prof. ME invested
$160,000 hoping to have $420,000 available 12 years later when the
first child started college. However,
the account’s balance is now only $140,000. Let’s figure out what
is needed to get Prof. ME’s
college savings plan back on track.
a. What was the original annual rate of return needed to reach
Prof. ME’s goal when he started
the fund 2 years ago?
b. Now with only $140,000 in the fund and 10 years remaining until
his first child starts college,
what annual rate of return would the fund have to earn to reach
Prof. ME’s $420,000
goal if he adds nothing to the account?
c. Shocked by his experience of the past 2 years, Prof. ME feels
the college mutual fund has
invested too much in stocks. He wants a low-risk fund in order to
ensure he has the necessary
$420,000 in 10 years, and he is willing to make end-of-the-month
deposits to the fund
as well. He later finds a fund that promises to pay a guaranteed
return of 6 percent compounded
monthly. Prof. ME decides to transfer the $140,000 to this new
fund and make the
necessary monthly deposits. How large of a monthly deposit must
Prof. ME make into this
new fund to meet his $420,000 goal?
d. Now Prof. ME gets sticker shock from the necessary monthly
deposit he has to make into
the guaranteed fund in the preceding question. He decides to
invest the $140,000 today and
$500 at the end of each month for the next 10 years into a fund
consisting of 50 percent
stock and 50 percent bonds and hope for the best. What annual rate
of return would the
fund have
to earn in order to reach Prof. ME’s $420,000 goal?
