9) The British government has a consol bond outstanding that pays ₤100 in interest each year.
Assuming that the current interest rate in Great Britain is 5% and that you will receive your first interest
payment one year from now, then the value of the consol bond is closest to:
A) ₤1000
B) ₤1100
C) ₤2100
D) ₤2000
10) The British government has a consol bond outstanding that pays ₤100 in interest each year.
Assuming that the current interest rate in Great Britain is 5% and that you will receive your first interest
payment immediately upon purchasing the consol bond, then the value of the consol bond is closest to:
A) ₤2000
B) ₤2100
C) ₤1000
D) ₤1100
11) If the current rate of interest is 8%, then the present value of an investment that pays $1000 per year
and lasts 20 years is closest to:
A) $18,519
B) $45,761
C) $9818
D) $20,000
12) If the current rate of interest is 8%, then the future value 20 years from now of an investment that
pays $1000 per year and lasts 20 years is closest to:
A) $45,762
B) $36,725
C) $9818
D) $93,219
13) Suppose that a young couple has just had their first baby and they wish to insure that enough
money will be available to pay for their child’s college education. They decide to make deposits into an
educational savings account on each of their daughter’s birthdays, starting with her first birthday.
Assume that the educational savings account will return a constant 7%. The parents deposit $2000 on
their daughter’s first birthday and plan to increase the size of their deposits by 5% each year. Assuming
that the parents have already made the deposit for their daughter’s 18th birthday, then the amount
available for the daughter’s college expenses on her 18th birthday is closest to:
A) $42,825
B) $97,331
C) $67,998
D) $103,063
14) Since your first birthday, your grandparents have been depositing $1000 into a savings account on
every one of your birthdays. The account pays 4% interest annually. Immediately after your
grandparents make the deposit on your 18th birthday, the amount of money in your savings account
will be closest to:
A) $25,645
B) $36,465
C) $12,659
D) $18,000
15) Consider a growing perpetuity that will pay $100 in one year. Each year after that, you will receive
a payment on the anniversary of the last payment that is 6% larger than the last payment. This pattern
of payments will continue forever. If the interest rate is 11%, then the value of this perpetuity is closest
to:
A) $1667
B) $588
C) $2000
D) $909
16) You are thinking about investing in a mine that will produce $10,000 worth of ore in the first year.
As the ore closest to the surface is removed it will become more difficult to extract the ore. Therefore,
the value of the ore that you mine will decline at a rate of 8% per year forever. If the appropriate
interest rate is 6%, then the value of this mining operation is closest to:
A) $71,429
B) $500,000
C) $166,667
D) This problem cannot be solved.
Use the information for the question(s) below.
Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your
current salary is $45,000 and you expect your salary to increase at a rate of 5% per year as long as you
work. To save for your retirement, you plan on making annual contributions to a retirement account.
Your first contribution will be made on your 31st birthday and will be 8% of this year’s salary.
Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the
rate of interest is 7%.
17) The present value (at age 30) of your retirement savings is closest to:
A) $87,000
B) $108,000
C) $46,600
D) $75,230
18) The future value at retirement (age 65) of your savings is closest to:
A) $497,530
B) $928,895
C) $1,263,236
D) $108,000
19) You work for a pharmaceutical company that has developed a new drug. The patent on the drug
will last for 17 years. You expect that the drug will produce cash flows of $10 million in its first year
and that this amount will grow at a rate of 4% per year for the next 17 years. Once the patent expires,
other pharmaceutical companies will be able to produce generic equivalents of your drug and
competition will drive any future profits to zero. If the interest rate is 12% per year, then the present
value of producing this drug is closest to:
A) $71 million
B) $90 million
C) $170 million
D) $105 million
20) Your son is about to start kindergarten in a private school. Currently, the tuition is $12,000 per year,
payable at the start of the school year. You expect annual tuition increases to average 6% per year over
the next 13 years. Assuming that you son remains in this private school through high school and that
your current interest rate is 7%, then the present value of your son’s private school education is closest
to:
A) $332,300
B) $137,900
C) $155,800
D) $156,000
21) Your son is about to start kindergarten in a private school. Currently, the tuition is $12,000 per year,
payable at the start of the school year. You expect annual tuition increases to average 6% per year over
the next 13 years. Assuming that your son remains in this private school through high school and that
your current interest rate is 6%, then the present value of your son’s private school education is closest
to:
A) $106,230
B) $156,000
C) $137,900
D) This problem cannot be solved.
22) If the appropriate interest rate is 8%, then present value of $500 paid at the end of each of the next 40
years is closest to:
A) $23
B) $5962
C) $6439
D) $20,0000
23) If the appropriate interest rate is 8%, then present value of $500 paid at the beginning of each of the
next 40 years is closest to:
A) $23
B) $5962
C) $6439
D) $20,000
24) Dagny Taggart is a graduating college senior and she is considering the costs of going to medical
school. Beginning next fall, Dagny expects medical school tuition to run $45,000 for the first year and
she estimates that tuition will increase by 6% each year. If Dagny is able to invest her money in an
account paying 8% interest per year, then the present value to Dagny of four years of medical school
tuition is closest to:
A) $149,045
B) $155,930
C) $162,095
D) $180,000
25) You are offered an investment opportunity that costs you $28,000, has an NPV of $2278, lasts for
three years, has interest rate of 10%, and produces the following cash flows:
The missing cash flow from year 2 is closest to:
A) $12,500
B) $12,000
C) $13,000
D) $10,000
26) Define the following terms:
(a) perpetuity
(b) annuity
(c) growing perpetuity
(d) growing annuity
27) How do you calculate (mathematically) the present value of a(n):
(a) perpetuity
(b) annuity
(c) growing perpetuity
(d) growing annuity
Use the information for the question(s) below.
Suppose that a young couple has just had their first baby and they wish to ensure that enough money
will be available to pay for their child’s college education. Currently, college tuition, books, fees, and
other costs, average $12,500 per year. On average, tuition and other costs have historically increased at
a rate of 4% per year.
28) Assuming that college costs continue to increase an average of 4% per year and that all her college
savings are invested in an account paying 7% interest, then the amount of money she will need to have
available at age 18 to pay for all four years of her undergraduate education is closest to:
Use the information for the question(s) below.
Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your
current salary is $45,000 and you expect your salary to increase at a rate of 5% per year as long as you
work. To save for your retirement, you plan on making annual contributions to a retirement account.
Your first contribution will be made on your 31st birthday and will be 8% of this year’s salary.
Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the
rate of interest is 7%.
29) The future value at retirement (age 65) of your savings is:
30) Assume that you are 30 years old today, and that you are planning on retiring at age 65. Your
current salary is $45,000 and you expect your salary to increase at a rate of 5% per year as long as you
work. To save for your retirement, you plan on making annual contributions to a retirement account.
Your first contribution will be made on your 31st birthday and will be 8% of this year’s salary.
Likewise, you expect to deposit 8% of your salary each year until you reach age 65. At retirement (age
65) you will begin withdrawing equal annual payments to pay for your living expenses during
retirement (on your 65th birthday). If you expect to die one day before your 101st birthday (Your last
withdraw will be on your 100th birthday) and if the annual rate of return is 7%, then how much money
will you have to spend in each of your golden years of retirement?
4.6 Using an Annuity Spreadsheet or Calculator
1) Which of the following is NOT a valid time value of money function in Excel?
A) PMT
B) NPER
C) I
D) FV
2) Suppose that you deposit $10,000 in an account that pays 6% interest and you want to know how
much will be in your account at the end of 10 years. To solve this problem in Microsoft Excel, you
would use which of the following Excel formulas?
A) =FV(.06,10000,0,10)
B) =PV(.06,10000,0,10)
C) =FV(.06,10,0,10000)
D) =PV(.06,10,0,10000)
3) Suppose that you are considering an investment that will pay you $4000 per year for the next five
years. The appropriate rate of interest is 5%. You want to know the present value of the cash flows
from this investment. To solve this problem in Microsoft Excel, you would use which of the following
excel formulas?
A) =PV(.05,5,4000,0,0)
B) =PV(.05,5,4000,0,1)
C) =PV(5,.05,4000,0)
D) =PV(5,5,4000,0)
4) Francisco d’Anconia is considering an investment opportunity that costs $10,000 today and will pay
$11,500 in two years. The IRR of this opportunity is closest to:
A) 7.25%
B) 7.50%
C) 10.00%
D) 15.00%
5) Henry Rearden is saving for retirement and has determined that to live comfortably he must save $3
million by his 65th birthday. Henry just turned 30 today, and he has decided that starting today and
continuing on every birthday up to and including his 65th birthday, he will deposit the same amount
into an individual retirement account (IRA). If Henry can earn 8% on his IRA, then the amount he must
set aside each year to make sure that he will have $3 million in his account on his 65th birthday is
closest to:
A) $16,035
B) $17,410
C) $83,335
D) $85,715
4.7 Non-Annual Cash Flows
1) You are interested in purchasing a new automobile that costs $35,000. The dealership offers you a
special financing rate of 6% APR (0.5%) per month for 48 months. Assuming that you do not make a
down payment on the auto and you take the dealer’s financing deal, then your monthly car payments
would be closest to:
A) $729
B) $822
C) $842
D) $647
2) You are considering purchasing a new home. You will need to borrow $250,000 to purchase the
home. A mortgage company offers you a 15 year fixed rate mortgage (180 months) at 9% APR (0.75%
month). If you borrow the money from this mortgage company, your monthly mortgage payment will
be closest to:
A) $2585
B) $660
C) $2535
D) $1390
3) If the current rate of interest is 8% APR, then the present value of an investment that pays $250 per
quarter and lasts 20 years is closest to:
A) $18,519
B) $48,443
C) $9936
D) $20,000
4) If the current rate of interest is 8% APR, then the future value of an investment that pays $250 per
quarter and lasts 20 years is closest to:
A) $18,519
B) $48,443
C) $9936
D) $20,000
5) If the current rate of interest is 8% APR, then the future value of an investment that pays $500 every
two years and lasts 20 years is closest to:
A) $11,000
B) $10,661
C) $22,881
D) $20,000
4.8 Solving for the Cash Payments
1) The British government has just issued a new consol bond that sells for £1000 and pays interest of 8%.
The annual interest payment on this bond must be:
A) £80
B) £8
C) £1000
D) £12,500
2) Taggart Transcontinental currently has a bank loan outstanding that requires it to make three annual
payments at the end of the next three years or to skip making the next two payments in lieu of making
one large payment at the end of the loan’s term in three years in the amount of $3,184,000. If the interest
rate on the loan is 6%, then the annual payment the bank will require to make Taggart Transcontinental
indifferent between the two forms of payments is closest to:
A) $2,673,000
B) $2,000,000
C) $1,673,000
D) $1,000,000
3) You are saving for retirement. To live comfortably, you decide that you will need $2.5 million dollars
by the time you are 65. If today is your 30th birthday, and you decide, starting today, and on every
birthday up to and including your 65th birthday, that you will deposit the same amount into your
savings account. Assuming the interest rate is 5%, the amount that you must set aside each year on
your birthday is closest to:
A) $71,430
B) $27,680
C) $26,100
D) $26,260
4) You are saving for retirement. To live comfortably, you decide that you will need $2.5 million dollars
by the time you are 65. If you assume you are able to do that, and will live 20 more years (until age 85),
the amount you can withdraw in each of those years at an interest rate of 5% before your retirement
fund is empty is closest to:
A) $72,987
B) $75,606
C) $197,987
D) $200,606
4.9 The Internal Rate of Return
1) You have an investment opportunity that will cost you $10,000 today, but return $12,500 to you in
one year. The IRR of this investment opportunity is closest to:
A) 80%
B) 125%
C) 20%
D) 25%
2) You are looking for a new truck and see the following advertisement. “Own a new truck! No money
down. Just five easy annual payments of $8000.” You know that you can get the same truck from the
dealer across town for only $31,120. The interest rate for the deal advertised is closest to:
A) 9%
B) 8%
C) 8.5%
D) 10%
3) You are considering investing in a zero coupon bond that will pay you its face value of $1000 in ten
years. If the bond is currently selling for $485.20, then the IRR for investing in this bond is closest to:
A) 12%
B) 8.0%
C) 7.5%
D) 10%
4) You are considering investing in a security that will pay you $80 in interest at the end of each of the
next 10 years. If this security is currently selling for $588.81, then the IRR for investing in this security is
closest to:
A) 6.0%
B) 7.0%
C) 6.5%
D) 5.0%
Use the following information to answer the question(s) below.
Nielson Motors is considering an opportunity that requires an investment of $1,000,000 today and will
provide $250,000 one year from now, $450,000 two years from now, and $650,000 three years from now.
5) The Internal Rate of return of this project is closest to:
A) 10.2%
B) 12.2%
C) 14.2%
D) 16.2%
4.10 Appendix: Solving for the Number of Periods
1) After your grandmother retired, she purchased an annuity contract for $250,000 that will pay her
$25,000 at the end of every year until she dies. The appropriate interest rate for this annuity is 8%. The
number of years that your grandmother must live in order to get more value out of the annuity than
what she paid for it is closest to:
A) 21
B) 16
C) 8
D) 10
2) You have an $8000 balance on your credit card, which charges 12% interest annually (1% per month).
If you can afford to pay $100 per month, how many months will it take to pay the credit card in full?
A) 170 months
B) 14 months
C) 162 months
D) You will never get the card paid off at that rate.
3) You have an $8000 balance on your credit card, which charges 18% interest annually (1% per month).
If you can afford to pay $100 per month, how many months will it take to pay the credit card in full?
A) 170 months
B) 14 months
C) 162 months
D) You will never get the card paid off at that rate.