Financial Planning Problems

| August 14, 2017

4-21. When you purchased your
house, you took out a 30-year annual-payment mortgage with an
interest rate of 6% per year. The
annual payment on the mortgage is $12,000. You have just
made a payment and have now
decided to pay the mortgage off by repaying the outstanding
balance. What is the payoff amount
a. You have lived in the house for
12 years (so there are 18 years left on the mortgage)?
b. You have lived in the house for
20 years (so there are 10 years left on the mortgage)?
c. You have lived in the house for
12 years (so there are 18 years left on the mortgage) and you
decide to pay off the mortgage
the twelfth payment is due?
4-22. You are 25 years old and
decide to start saving for your retirement. You plan to save $5000 at
the end of each year (so the first
deposit will be one year from now), and will make the last
deposit when you retire at age 65.
Suppose you earn 8% per year on your retirement savings.
a. How much will you have saved
for retirement?
b. How much will you have saved if
you wait until age 35 to start saving (again, with your first
deposit at the end of the year)?

4-23. Your grandmother has been
putting $1000 into a savings account on every birthday since your
first (that is, when you turned
1). The account pays an interest rate of 3%. How much money will
be in the account on your 18th
birthday immediately after your grandmother makes the deposit
on that birthday?

4-24. A rich relative has
bequeathed you a growing perpetuity. The first payment will occur in a year
and will be $1000. Each year after
that, you will receive a payment on the anniversary of the last
payment that is 8% larger than the
last payment. This pattern of payments will go on forever. If
the interest rate is 12% per year,
a. What is today’s value of the
b. What is the value of the
bequest immediately after the first payment is made?

4-25. You are thinking of building
a new machine that will save you $1000 in the first year. The
machine will then begin to wear
out so that the savingsdeclineat a rate of 2% per year forever.
What is the present value of the
savings if the interest rate is 5% per year?

4-26. You work for a
pharmaceutical company that has developed a new drug. The patent on the drug
will last 17 years. You expect
that the drug’s profits will be $2 million in its first year and that
this amount will grow at a rate of
5% per year for the next 17 years. Once the patent expires,
other pharmaceutical companies
will be able to produce the same drug and competition will
likely drive profits to zero. What
is the present value of the new drug if the interest rate is 10%
per year?

4-27. Your oldest daughter is
about to start kindergarten at a private school. Tuition is $10,000 per
year, payable at thebeginningof the school year. You expect to
keep your daughter in private
school through high school. You
expect tuition to increase at a rate of 5% per year over the 13
years of her schooling. What is
the present value of the tuition payments if the interest rate is 5%
per year? How much would you need
to have in the bank now to fund all 13 years of tuition?

4-28. A rich aunt has promised you
$5000 one year from today. In addition, each year after that, she
has promised you a payment (on the
anniversary of the last payment) that is 5% larger than the
last payment. She will continue to
show this generosity for 20 years, giving a total of 20
payments. If the interest rate is
5%, what is her promise worth today?

4-29. You are running a hot
Internet company. Analysts predict that its earnings will grow at 30% per
year for the next five years.
After that, as competition increases, earnings growth is expected to
slow to 2% per year and continue
at that level forever. Your company has just announced
earnings of $1,000,000. What is
the present value of all future earnings if the interest rate is 8%?
(Assume all cash flows occur at
the end of the year.)
4-30. Your brother has offered to
give you $100, starting next year, and after that growing at 3% for
the next 20 years. You would like
to calculate the value of this offer by calculating how much
money you would need to deposit in
the local bank so that the account will generate the same
cash flows as he is offering you.
Your local bank will guarantee a 6% annual interest rate so long
as you have money in the account.
a. How much money will you need to
deposit into the account today?
b. Using an Excel spreadsheet,
show explicitly that you can deposit this amount of money into
the account, and every year
withdraw what your brother has promised, leaving the account
with nothing after the last

4-31. You have decided to buy a
perpetuity. The bond makes one payment at the end of every year
forever and has an interest rate
of 5%. If you initially put $1000 into the bond, what is the
payment every year?

4-32. You are thinking of
purchasing a house. The house costs $350,000. You have $50,000 in cash that
you can use as a down payment on
the house, but you need to borrow the rest of the purchase
price. The bank is offering a
30-year mortgage that requires annual payments and has an
interest rate of 7% per year. What
will your annual payment be if you sign up for this mortgage?

4-33. You are thinking about
buying a piece of art that costs $50,000. The art dealer is proposing the
following deal: He will lend you
the money, and you will repay the loan by making the same
payment every two years for the
next 20 years (i.e., a total of 10 payments). If the interest rate is
4%, how much will you have to pay
every two years?

4-34. You would like to buy the
house and take the mortgage described in Problem 32. You can afford
to pay only $23,500 per year. The
bank agrees to allow you to pay this amount each year, yet still
borrow $300,000. At the end of the
mortgage (in 30 years), you must make aballoonpayment;
that is, you must repay the
remaining balance on the mortgage. How much will this balloon
payment be?

4-35. You are saving for
retirement. To live comfortably, you decide you will need to save $2 million
by the time you are 65. Today is
your 30th birthday, and you decide, starting today and
continuing on every birthday up to
and including your 65th birthday, that you will put the same
amount into a savings account. If
the interest rate is 5%, how much must you set aside each year
to make sure that you will have $2
million in the account on your 65th birthday?

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