# Financial Planning Problems

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

if

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

immediatelybefore

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 todayâs value of the

bequest?

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 drugâs 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

withdrawal.

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?