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Management: Financial Principles and Applications, 11e (Titman)
Chapter 6 The Time Value of Money-Annuities and Other Topics
6.1 Annuities
1) You wish to borrow $2,000 to be repaid in 12 monthly installments of $189.12. The annual
interest rate is:
A) 24%.
B) 8%.
C) 18%.
D) 12%.
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
2) If you have $20,000 in an account earning 8% annually, what constant amount could you
withdraw each year and have nothing remaining at the end of five years?
A) $3,525.62
B) $5,008.76
C) $3,408.88
D) $2,465.78
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
3) If you invest $750 every six months at 8% compounded semi-annually, how much would you
accumulate at the end of 10 years?
A) $10,065
B) $10,193
C) $22,334
D) $21,731
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
1
Copyright 2011 Pearson Education, Inc.
4) A commercial bank will loan you $7,500 for two years to buy a car. The loan must be repaid
in 24 equal monthly payments. The annual interest rate on the loan is 12% of the unpaid balance.
What is the amount of the monthly payments?
A) $282.43
B) $390.52
C) $369.82
D) $353.05
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
5) Your company has received a $50,000 loan from an industrial finance company. The annual
payments are $6,202.70. If the company is paying 9% interest per year, how many loan
payments must the company make?
A) 15
B) 13
C) 12
D) 19
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
6) ________ annuities involve depositing money at the end of the period and allowing it to grow.
A) Discount
B) Compound
C) Annuity due
D) Both B and C
Diff: 2
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
7) When comparing annuity due to ordinary annuities, annuity due annuities will have higher:
A) present values.
B) annuity payments.
C) future values.
D) both A and C.
E) all of the above.
Diff: 3
Topic: 6.1 Annuities
Keywords: annuity due
Principles: Principle 1: Money Has a Time Value
2
Copyright 2011 Pearson Education, Inc.
8) Gina Dare, who wants to be a millionaire, plans to retire at the end of 40 years. Gina's plan is
to invest her money by depositing into an IRA at the end of every year. What is the amount that
she needs to deposit annually in order to accumulate $1,000,000? Assume that the account will
earn an annual rate of 11.5%. Round off to the nearest $1.
A) $1,497
B) $5,281
C) $75
D) $3,622
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
9) Francis Peabody just won the $89,000,000 California State Lottery. The lottery offers the
winner a choice of receiving the winnings in a lump sum or in 26 equal annual installments to be
made at the beginning of each year. Assume that funds would be invested at 7.65%. Francis is
trying to decide whether to take the lump sum or the annual installments. What is the amount of
the lump sum that would be exactly equal to the present value of the annual installments? Round
off to the nearest $1.
A) $89,000,000
B) $38,163,612
C) $13,092,576
D) $41,083,128
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
10) As time increases for an amortized loan, the ________ decreases.
A) interest paid per payment
B) principal paid per payment
C) the outstanding loan balance
D) both A and C
E) all of the above
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
3
Copyright 2011 Pearson Education, Inc.
11) What is the present value of an annuity of $27 received at the beginning of each year for the
next six years? The first payment will be received today, and the discount rate is 10% (round to
nearest $10).
A) $120
B) $130
C) $100
D) $110
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
12) What is the present value of $150 received at the beginning of each year for 16 years? The
first payment is received today. Use a discount rate of 9%, and round your answer to the nearest
$10.
A) $1,360
B) $1,480
C) $1,250
D) $1,210
Diff: 2
Topic: 6.1 Annuities
Keywords: annuity due
Principles: Principle 1: Money Has a Time Value
13) What is the present value of $250 received at the beginning of each year for 21 years?
Assume that the first payment is received today. Use a discount rate of 12%, and round your
answer to the nearest $10.
A) $1,870
B) $2,090
C) $2,117
D) $3,243
Diff: 2
Topic: 6.1 Annuities
Keywords: annuity due
Principles: Principle 1: Money Has a Time Value
4
Copyright 2011 Pearson Education, Inc.
14) What is the present value of an annuity of $12 received at the end of each year for seven
years? Assume a discount rate of 11%. The first payment will be received one year from today
(round to the nearest $1).
A) $25
B) $40
C) $57
D) $118
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
15) What is the present value of an annuity of $100 received at the end of each year for seven
years? The first payment will be received one year from today (round to nearest $10). The
discount rate is 13%.
A) $440
B) $43
C) $500
D) $1,040
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
16) What is the present value of $27 received at the end of each year for five years? Assume a
discount rate of 9%. The first payment will be received one year from today (round to the nearest
$1).
A) $42
B) $114
C) $88
D) $105
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
5
Copyright 2011 Pearson Education, Inc.
17) What is the present value of $300 received at the beginning of each year for five years?
Assume that the first payment is not received until the beginning of the third year (thus the last
payment is received at the beginning of the seventh year). Use a 10% discount rate, and round
your answer to the nearest $100.
A) $1,100
B) $1,000
C) $900
D) $1,200
Diff: 3
Topic: 6.1 Annuities
Keywords: annuity due
Principles: Principle 1: Money Has a Time Value
18) Ingrid Birdman can earn a nominal annual rate of return of 12%, compounded semiannually.
If Ingrid made 40 consecutive semiannual deposits of $500 each, with the first deposit being
made today, how much will she accumulate at the end of Year 20? Round off to the nearest $1.
A) $52,821
B) $57,901
C) $82,024
D) $64,132
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
19) Charlie Stone wants to retire in 30 years, and he wants to have an annuity of $1,000 a year
for 20 years after retirement. Charlie wants to receive the first annuity payment at the end of the
30th year. Using an interest rate of 10%, how much must Charlie invest today in order to have
his retirement annuity (round to the nearest $10)?
A) $500
B) $490
C) $540
D) $570
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
6
Copyright 2011 Pearson Education, Inc.
20) It is January 1st and Darwin Davis has just established an IRA (Individual Retirement
Account). Darwin will put $1,000 into the account on December 31st of this year and at the end
of each year for the following 39 years (40 years total). How much money will Darwin have in
his account at the beginning of the 41st year? Assume that the account pays 12% interest
compounded annually, and round to the nearest $1,000.
A) $93,000
B) $766,000
C) $767,000
D) $850,000
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
21) If you put $510 in a savings account at the beginning of each year for 30 years, how much
money will be in the account at the end of the 30th year? Assume that the account earns 5%, and
round to the nearest $100.
A) $33,300
B) $32,300
C) $33,900
D) None of the above
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
22) If you put $10 in a savings account at the beginning of each year for 11 years, how much
money will be in the account at the end of the 11th year? Assume that the account earns 11%,
and round to the nearest $100.
A) $220
B) $200
C) $190
D) $180
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
7
Copyright 2011 Pearson Education, Inc.
23) If you put $310 in a savings account at the beginning of each year for 10 years, how much
money will be in the account at the end of the 10th year? Assume that the account earns 5.5%,
and round to the nearest $100.
A) $3,800
B) $3,900
C) $4,000
D) $4,200
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
24) How much money must you pay into an account at the beginning of each of 30 years in order
to have $10,000 at the end of the 30th year? Assume that the account pays 11% per annum, and
round to the nearest $1.
A) $39
B) $46
C) $50
D) None of the above
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
25) How much money must you pay into an account at the beginning of each of 20 years in order
to have $10,000 at the end of the 20th year? Assume that the account pays 12% per annum, and
round to the nearest $1.
A) $1,195
B) $111
C) $124
D) $139
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
8
Copyright 2011 Pearson Education, Inc.
26) How much money must you pay into an account at the beginning of each of five years in
order to have $5,000 at the end of the fifth year? Assume that the account pays 12% per year,
and round to the nearest $10.
A) $700
B) $1,390
C) $1,550
D) $790
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
27) How much money must you pay into an account at the beginning of each of 11 years in order
to have $5,000 at the end of the 11th year? Assume that the account pays 8% per year, and round
to the nearest $1.
A) $700
B) $257
C) $300
D) $278
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
Use the following information in solving the following question(s).
You are going to pay $100 into an account at the beginning of each of the next 40 years. At the
beginning of the 41st year, you buy a 30-year annuity whose first payment comes at the end of
the 41st year (the account pays 12%).
28) How much money will be in the account at the end of year 40 (round to the nearest $1,000)?
A) $77,000
B) $86,000
C) $69,000
D) $93,000
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
9
Copyright 2011 Pearson Education, Inc.
29) How much will you receive at the end of the 41st year (i.e., the first annuity payment)?
Round to the nearest $100.
A) $93,000
B) $7,800
C) $11,400
D) $10,700
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
30) A retirement plan guarantees to pay you or your estate a fixed amount for 20 years. At the
time of retirement, you will have $31,360 to your credit in the plan. The plan anticipates earning
8% interest annually over the period you receive benefits. How much will your annual benefits
be, assuming the first payment occurs one year from your retirement date?
A) $682
B) $6,272
C) $2,000
D) $3,194
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
31) SellUCars, Inc. offers you a car loan at an annual interest rate of 8% compounded quarterly.
What is the annual percentage yield of the loan?
A) 8.00%
B) 8.24%
C) 8.32%
D) 8.44%
Diff: 1
Topic: 6.1 Annuities
Keywords: effective annual rate
Principles: Principle 1: Money Has a Time Value
10
Copyright 2011 Pearson Education, Inc.
32) George and Barbara will be retiring in four years and would like to buy a lake house. They
estimate that they will need $150,000 at the end of four years to buy this house. They want to
make four equal annual payments into an account at the end of each year. If they can earn 16%
on their money, compounded annually, over the next four years, how much must they invest at
the end of each year for the next four years to have accumulated $150,000 by retirement?
A) $25,523
B) $29,606
C) $46,212
D) $43,500
E) $37,500
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
33) You have been accepted to study gourmet cooking at Le Cordon Bleu Culinary Institute in
Paris, France. You will need $15,000 every six months (beginning six months from now) for the
next three years to cover tuition and living expenses. Mom and Dad have agreed to pay for your
education. They want to make one deposit now in a bank account earning 6% interest,
compounded semiannually, so that you can withdraw $15,000 every six months for the next three
years. How much must they deposit now?
A) $97,026
B) $73,760
C) $90,000
D) $81,258
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
34) Horace and Myrtle want to buy a house. Their banker offered them a fully amortizing
$95,000 loan at a 12% annual rate for 20 years. What will their monthly payment be if they make
equal monthly installments over the next 20 years?
A) $1,046
B) $749
C) $1,722
D) $1,346
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
11
Copyright 2011 Pearson Education, Inc.
35) Harold Hawkins bought a home for $320,000. He made a down payment of $45,000; the
balance will be paid off over 30 years at a 6.775% rate of interest. How much will Harold's
monthly payments be? Round off to the nearest $1.
A) $1,450
B) $1,788
C) $3,200
D) $1,682
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
36) You buy a race horse, which has a winning streak for four years, bringing in $500,000 per
year, and then it dies of a heart attack. If you paid $1,518,675 for the horse four years ago, what
was your annual return over this four-year period?
A) 8%
B) 33%
C) 18%
D) 12%
Diff: 2
Topic: 6.1 Annuities
Keywords: internal rate of return
Principles: Principle 1: Money Has a Time Value
37) You are considering a home loan with monthly payments at an annual percentage yield of
5.116%. What is the quoted rate of interest on the loan?
A) 4.5%
B) 4.75%
C) 5%
D) 6%
Diff: 2
Topic: 6.1 Annuities
Keywords: effective annual rate
Principles: Principle 1: Money Has a Time Value
12
Copyright 2011 Pearson Education, Inc.
38) You deposited $2,000 in a bank account paying 6% on January 1, 2004, and then you made
$2,000 deposits on January 1 in 2005 and 2006. Which of the following expressions will
calculate your bank balance just after the last payment was deposited?
A) FV = $2,000[1.06]-1 + $2,000[1.06]-2 + $2,000[1.06]-3
B) FV = $2,000[1.06]1 + $2,000[1.06]2 + $2,000[1.06]3
C) FV = $2,000[1.06]0 + $2,000[1.06]1 + $2,000[1.06]2
D) FV = $2,000[1.06]-0 + $2,000[1.06]-1 + $2,000[1.06]-2 + $1,000[1.06]-3
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
39) Harry just bought a new four-wheel-drive Jeep Cherokee for his lumber business. The price
of the vehicle was $35,000, of which he made a $5,000 down payment and took out an amortized
loan for the rest. His local bank made the loan at 12% interest for five years. He is to pay back
the principal and interest in five equal annual installments beginning one year from now.
Determine the amount of Harry's annual payment.
A) $8,322
B) $9,600
C) $9,709
D) $6,720
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
40) Your investment goal is to have $3,000,000 in 40 years for retirement. You decide to invest
in a mutual fund today that pays 12% per year compounded monthly. How much must you invest
at the end of each month to meet your investment goal? Round to the nearest $1.
A) $245
B) $255
C) $285
D) $305
E) $315
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
13
Copyright 2011 Pearson Education, Inc.
41) You have borrowed $70,000 to buy a sports car. You plan to make monthly payments over a
15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the
total amount of interest dollars you will pay the bank over the life of the loan. Round to the
nearest dollar and assume end-of-month payments.
A) $47,451
B) $51,644
C) $54,776
D) $57,798
Diff: 3
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
42) You have borrowed $70,000 to buy rental property. You plan to make monthly payments
over a 15-year period. The bank has offered you a 9% interest rate compounded monthly.
Calculate the principal paid to the bank in month two of the loan. Assume end-of-period
payments.
A) $184.01
B) $186.38
C) $188.46
D) $190.64
E) $192.73
Diff: 3
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
43) A friend of yours plans to begin saving for retirement by depositing $2,000 at the end of each
year for the next 25 years. If she can earn 10% annually on her investment, how much will she
have accumulated at the end of 25 years?
A) $50,000
B) $196,692
C) $100,000
D) $216,361
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
14
Copyright 2011 Pearson Education, Inc.
44) How much must you deposit at the end of each of the next 10 years in a savings account
paying 5% annually in order to have $10,000 saved by the end of the 10th year?
A) $1,000
B) $1,638
C) $1,500
D) $795
Diff: 1
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
45) What is the value today of an investment that pays $500 every year at year-end during the
next 15 years if the annual interest rate is 9%?
A) $4,030.50
B) $7,500.00
C) $3,500.00
D) $7,000.00
Diff: 1
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
46) How much would an investor be willing to pay today for an investment that returns $1,000
every year at year-end for five years if he wants to earn a 10% annual return on the investment?
A) $1,000
B) $3,791
C) $5,000
D) $7,700
Diff: 1
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
47) A friend of yours would like you to lend him $5,000 today to be paid back in 5 annual
payments. What would be the equal annual end-of-year payment on this loan if you charge your
friend 7% interest?
A) $869.45
B) $1,000.00
C) $1,219.51
D) $1,350.00
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
15
Copyright 2011 Pearson Education, Inc.
48) Recently you borrowed money for a new car. The loan amount is $15,000 to be paid back in
equal annual payments which begin today, and will continue to be payable at the beginning of
each year for a total of five years. Interest on the loan is 8%. What is the amount of the loan
payment?
A) $3,756.85
B) $4,200.00
C) $3,478.31
D) $3,000.00
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
49) A friend of yours borrows $19,500 from the bank at 8% annually to be repaid in 10 equal
annual end-of-year installments. The interest paid on this loan in year three is:
A) $1,336.01.
B) $1,560.00.
C) $2,906.11.
D) $1,947.10.
Diff: 2
Topic: 6.1 Annuities
Keywords: interest paid
Principles: Principle 1: Money Has a Time Value
50) If a loan of $10,000 is paid back in equal annual end-of-year payments of $2,570.69 during
the next five years, what is the annual interest rate on the loan?
A) 2%
B) 5%
C) 9%
D) 12%
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
16
Copyright 2011 Pearson Education, Inc.
51) What is the present value of an investment that pays $10,000 every year at year-end for the
next five years and $15,000 every year at year-end for years six through 10? The annual rate of
interest for the investment is 9%.
A) $125,000.00
B) $97,250.00
C) $135,173.00
D) $76,827.50
Diff: 2
Topic: 6.1 Annuities
Keywords: present value income stream
Principles: Principle 1: Money Has a Time Value
52) Congratulations. You just won the California State Lottery. The amount awarded is paid in
20 equal annual installments, at the beginning of each year. You can invest your money at 6.6%,
compounded annually. You have calculated that the lottery is worth $20,975,400 today. How
much was the amount awarded?
A) $75,310,294
B) $36,000,000
C) $81,047,770
D) $42,000,000
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
53) If you have $375,000 in an account earning 9% annually, what constant amount could you
withdraw each year and have nothing remaining at the end of 20 years?
A) $7,500
B) $18,750
C) $66,912
D) $5,575
E) $41,080
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
17
Copyright 2011 Pearson Education, Inc.
54) You wish to borrow $12,000 to be repaid in 60 monthly installments of $257.93. The annual
interest rate is:
A) 10.50%.
B) 12.75%.
C) 15.25%.
D) 6.50%.
E) 8.80%.
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
55) You wish to purchase a condo at a cost of $175,000. You are able to make a down payment
of $35,000 and will borrow $140,000 for 30 years at an interest rate of 7.25%. How much is your
monthly payment?
A) $650
B) $955
C) $1,092
D) $1,023
E) $875
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
56) Suppose that you wish to save for your child's college education by opening up an
educational IRA. You plan to deposit $100 per month into the IRA for the next 18 years. Assume
that you will be able to earn 10%, compounded monthly, on your investment. How much will
you have accumulated at the end of 18 years?
A) $21,600
B) $54,719
C) $33,548
D) $85,920
E) $60,056
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
18
Copyright 2011 Pearson Education, Inc.
57) Edward Johnson decided to open up a Roth IRA. He will invest $1,800 per year for the next
35 years. Deposits to the Roth IRA will be made via a $150 payroll deduction at the end of each
month. Assume that Edward will earn 8.75% annual interest compounded monthly over the life
of the IRA. How much will he have at the end of 35 years?
A) $125,250
B) $250,321
C) $363,000
D) $414,405
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
58) What is a series of equal payments for a finite period of time called?
A) A perpetuity
B) An axiom
C) A lump sum
D) An annuity
Diff: 1
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
59) Which of the following statements is true?
A) The future value of an annuity would be greater if funds are invested at the beginning of each
period instead of at the end of each period.
B) An annuity is a series of equal payments that are made, or received, forever.
C) The effective annual rate (APR) of a loan is higher the less frequently payments are made.
D) The future value of an annuity would be greater if funds are invested at the end of each period
rather than at the beginning of each period.
Diff: 2
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
19
Copyright 2011 Pearson Education, Inc.
60) What is a series of equal payments to be received at the end of each period, for a finite period
of time, called?
A) A perpetuity
B) An annuity due
C) A cash cow
D) A deferred annuity
Diff: 1
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
61) What is a series of equal payments to be received at the beginning of each period, for a finite
period of time, called?
A) A perpetuity
B) An annuity due
C) A cash cow
D) A deferred annuity
Diff: 1
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
62) One characteristic of an annuity that is an equal sum of money is deposited or withdrawn
each period.
Diff: 1
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
63) The present value of an annuity increases as the discount rate increases.
Diff: 1
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
64) We can use the present value of an annuity formula to calculate constant annual loan
payments.
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
20
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65) A compound annuity involves depositing or investing a single sum of money and allowing it
to grow for a certain number of years.
Diff: 1
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
66) When repaying an amortized loan, the interest payments increase over time.
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
67) An amortized loan is a loan paid in unequal installments.
Diff: 1
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
68) A loan amortization schedule provides a breakdown of loan payments into principal and
interest payments.
Diff: 1
Topic: 6.1 Annuities
Keywords: present value
Principles: Principle 1: Money Has a Time Value
69) Holding all other variables constant, payment per period for an annuity due will be higher
than an ordinary annuity.
Diff: 3
Topic: 6.1 Annuities
Keywords: annuity due
Principles: Principle 1: Money Has a Time Value
70) If you have an opportunity cost of 10%, how much must you invest each year to have $4,000
accumulated in 10 years?
Answer:
$4,000 = A(15.937)
A = $250.99
Diff: 1
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
21
Copyright 2011 Pearson Education, Inc.
71) You have just received an endowment of $32,976. You plan to put the entire amount in an
account earning 8 percent compounded annually and to withdraw $4000 at the end of each year.
How many years can you continue to make the withdrawals?
Answer:
$32,976 = $4,000 PVIFA[8%, ? yr]
8.244 = PVIFA[8%, ? yr]
14 years
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
72) To repay a $2,000 loan from your bank, you promise to make equal payments every six
months for the next five years totaling $3,116.20. What annual rate of interest will you be
paying?
Answer:
Total payments of $3,116.20 indicates that each payment is $311.62.
$2,000 = $311.62 PVIFA[? %, 10 periods]
6.418 = PVIFA[? %, 10 periods]
i = 9%
Annual interest rate = (.09)(2) = .18 = 18%
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
73) You are saving money to buy a house. You will need $7,473.50 to make the down payment.
If you can deposit $500 per month in a savings account which pays 1% per month, how long will
it take you to save the $7,473.50?
Answer:
$7,473.50 = $500 FVIFA[1%, n periods]
14.947 = FVIFA[1%, n periods]
n = 14 months
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
22
Copyright 2011 Pearson Education, Inc.
74) You have a credit card with a balance of $18,000. The annual interest rate on the card is 18%
compounded monthly, and the minimum payment is $400 per month. If you pay only the
minimum payment each month and do not make any new charges on the card, how many years
will it take for you to pay off the $18,000 balance?
Answer:
Calculator steps:
18,000
PV
-400
PMT
18
I/yr or I
N = Approximately 75 months = 6.25 years
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
75) You have borrowed $70,000 to buy a speed boat. You plan to make monthly payments over
a 15-year period. The bank has offered you a 9% interest rate, compounded monthly. Create an
amortization schedule for the first two months of the loan.
Answer:
MO Beg
PMT
Int.
Princ.
End
1
$70,000
$709.99 $525
$184.99 $69,815.01
2
$69,815.01
$709.99 $523.61 $186.38 $69,628.63
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
76) You have just purchased a car from Friendly Sam. The selling price of the car is $6,500. If
you pay $500 down, then your monthly payments are $317.22. The annual interest rate is 24%.
How many payments must you make?
Answer:
$6,000 = $317.22 PVIFA[2%, ? periods]
18.914 = PVIFA[2%, ? periods] n = 24 months
Diff: 2
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
23
Copyright 2011 Pearson Education, Inc.
77) a.) If Sparco, Inc. deposits $150 at the end of each year for the next eight years in an account
that pays 5% interest, how much money will Sparco have at the end of eight years?
b.) Suppose Sparco decides that they need to have $5,300 at the end of the eight years. How
much will they have to deposit at the end of each year?
FV = $150 FVIFA [5%, 8 yr]
FV = $150 (9.549)
= $1,432.35
b. $5,300 = PMT FVIFA [5%, 8 yr]
$5,300 = PMT(9.549)
PMT = $555.03
Diff: 2
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
6.2 Perpetuities
1) What is a series of equal payments for an infinite period of time called?
A) A perpetuity
B) An axiom
C) A cash cow
D) An annuity
Diff: 1
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
2) You have just purchased a share of preferred stock for $50.00. The preferred stock pays an
annual dividend of $5.50 per share forever. What is the rate of return on your investment?
A) .055
B) .010
C) .110
D) .220
Diff: 2
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
24
Copyright 2011 Pearson Education, Inc.
3) The present value of a perpetuity decreases when the ________ decreases.
A) number of investment periods
B) annual discount rate
C) perpetuity payment
D) both B and C
Diff: 2
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
4) You are going to pay $800 into an account at the beginning of each of 20 years. The account
will then be left to compound for an additional 20 years. At the end of the 41st year you will
begin receiving a perpetuity from the account. If the account pays 14%, how much will you
receive each year from the perpetuity (round to nearest $1,000)?
A) $140,000
B) $150,000
C) $160,000
D) $170,000
Diff: 2
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
5) You are considering the purchase of XYZ Company's perpetual preferred stock which pays a
perpetual annual dividend of $8 per share. If the appropriate discount rate for this investment is
14%, what is the price of one share of this stock?
A) $7.02
B) $57.14
C) $36.43
D) Cannot be determined without maturity date
Diff: 2
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
25
Copyright 2011 Pearson Education, Inc.
6) Michael Bilkman has an opportunity to buy a perpetuity that pays $24,350 annually. His
required rate of return on this investment is 14.25%. At what price would Michael be indifferent
to buying or not buying the investment? Round off to the nearest $1.
A) $83,470
B) $170,877
C) $95,621
D) $121,709
Diff: 2
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
7) What is the present value of a $200 perpetuity when the discount rate is 10%?
A) $2,000
B) $20,000
C) $4,000
D) $40,000
Diff: 1
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
8) Your rich great, great aunt just passed away at the age of 91. She liked you more than she let
on and left you in her will. You will receive 100 British bonds that pay interest forever. The
amount of annual interest payments that you will receive is $5,000. If you could invest your
money at 4.25%, how much are these bonds worth today?
A) $64,480
B) $197,250
C) $250,000
D) $117,647
E) $55,000
Diff: 2
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
9) A bond paying interest of $120 per year forever is an example of a perpetuity.
Diff: 1
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
26
Copyright 2011 Pearson Education, Inc.
10) The formula for calculating the present value of a perpetuity is P = A/(1 + i).
Diff: 1
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
11) A perpetuity is an investment that continues forever but pays a different dollar amount each
year.
Diff: 1
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
12) The present value of a $100 perpetuity discounted at 5% is $1200.
Diff: 2
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
13) All else constant, an individual would be indifferent between receiving $2,000 today or
receiving a $200 perpetuity when the discount rate is 10% annually.
Diff: 2
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
14) If your opportunity cost is 12%, how much will you pay for a bond that pays $100 per year
forever?
Answer: PV = $100/.12 = $833.33
Diff: 1
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
27
Copyright 2011 Pearson Education, Inc.
15) What is the present value of the following perpetuities?
a. $600 discounted at 7%
b. $450 discounted at 12%
c. $1,000 discounted at 6%
d. $880 discounted at 9%
PV = $600/.07
PV = $8,571.43
b. PV = $450/.12
PV = $3,750
c. PV = $1,000/.06
PV = $16,666.67
d. PV = $880/.09
PV = $9,777.78
Diff: 2
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
6.3 Complex Cash Flow Streams
1) What is the value on 1/1/05 of the following cash flows? Use a 10% discount rate, and round
your answer to the nearest $10.
Date Cash Received Amount of Cash
1/1/07
$100
1/1/08
$200
1/1/09
$300
1/1/10
$400
1/1/11
$500
A) $490
B) $460
C) $970
D) $450
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
28
Copyright 2011 Pearson Education, Inc.
2) Consider the following cash flows:
Date Cash Received Amount of Cash
1/1/07
$100
1/1/08
$100
1/1/09
$500
1/1/10
$100
What is the value on 1/1/05 of the above cash flows? Use an 8% discount rate, and round your
answer to the nearest $10.
A) $600
B) $620
C) $630
D) $650
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
3) If you put $200 in a savings account at the beginning of each year for 10 years and then allow
the account to compound for an additional 10 years, how much will be in the account at the end
of the 20th year? Assume that the account earns 10%, and round to the nearest $10.
A) $8,300
B) $9,100
C) $8,900
D) $9,700
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
4) An investment is expected to yield $300 in three years, $500 in five years, and $300 in seven
years. What is the present value of this investment if our opportunity rate is 5%?
A) $735
B) $865
C) $885
D) $900
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
29
Copyright 2011 Pearson Education, Inc.
5) Jay Coleman just graduated. He plans to work for five years and then leave for the Australian
"Outback" country. He figures that he can save $3,500 a year for the first three years and $5,000
a year for the next two years. These savings will start one year from now. In addition, his family
gave him a $2,500 graduation gift. If he puts the gift, and the future savings when they start, into
an account that pays 7.75% compounded annually, what will his financial "stake" be when he
leaves for Australia five years from now? Round off to the nearest $1.
A) $36,082
B) $24,725
C) $30,003
D) $27,178
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value complex income stream
Principles: Principle 1: Money Has a Time Value
6) You are thinking of buying a miniature golf course. It is expected to generate cash flows of
$40,000 per year in years one through four and $50,000 per year in years five through eight. If
the appropriate discount rate is 10%, what is the present value of these cash flows?
A) $285,288
B) $167,943
C) $235,048
D) $828,230
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
7) You have been depositing money at the end of each year into an account drawing 8% interest.
What is the balance in the account at the end of year four if you deposited the following
amounts?
Year
End of Year Deposit
1
$350
2
$500
3
$725
4
$400
A) $1,622
B) $2,207
C) $2,384
D) $2,687
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value complex income stream
Principles: Principle 1: Money Has a Time Value
30
Copyright 2011 Pearson Education, Inc.
8) You want to travel to Europe to visit relatives when you graduate from college three years
from now. The trip is expected to cost a total of $10,000. Your parents have deposited $5,000 for
you in a CD paying 6% interest annually, maturing three years from now. Aunt Hilda has agreed
to finance the balance. If you are going to put Aunt Hilda's gift in an investment earning 10%
annually over the next three years, how much must she deposit now so you can visit your
relatives in three years?
A) $3,757
B) $3,039
C) $3,801
D) $3,345
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value
Principles: Principle 1: Money Has a Time Value
9) What is the present value of the following uneven stream of cash flows? Assume a 6%
discount rate and end-of-period payments. Round to the nearest whole dollar.
Year
Cash Flow
1
$3,000
2
$4,000
3
$5,000
A) $10,588
B) $11,461
C) $12,688
D) $13,591
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
10) As a part of your savings plan at work, you have been depositing $250 per quarter in a
savings account earning 8% interest compounded quarterly for the last 10 years. You will retire
in 15 years and want to increase your contribution each year from $1,000 to $2,000 per year, by
increasing your contribution every four months from $250 to $500. Additionally, you have just
inherited $10,000, which you plan to invest now to earn interest at 12% compounded annually
for the next 15 years. How much money will you have in savings when you retire 15 years from
now?
A) $126,862
B) $73,012
C) $161,307
D) $194,415
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value complex income stream
Principles: Principle 1: Money Has a Time Value
31
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11) Ronald Slump purchased a real estate investment with the following end-of-year cash flows:
Year
1
2
3
4
EOY Cash Flow
$200
$-350
$-430
$950
What is the present value of these cash flows if the appropriate discount rate is 20%?
A) $178
B) $160
C) $133
D) $767
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
12) You have just won a magazine sweepstakes and have a choice of three alternatives. You can
get $100,000 now, or $10,000 per year in perpetuity, or $50,000 now and $150,000 at the end of
10 years. If the appropriate discount rate is 12%, which option should you choose?
A) $100,000 now
B) $10,000 perpetuity
C) $50,000 now and $150,000 in 10 years
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
13) Your parents are planning to retire in Phoenix, AZ in 20 years. Currently, the typical house
that pleases your parents costs $200,000, but they expect inflation to increase the price of the
house at a rate of 4% over the next 20 years. In order to buy a house upon retirement, what must
they save each year in equal annual end-of-year deposits if they can earn 10% annually?
A) $21,910.00
B) $7,650.94
C) $10,000.00
D) $14,715.52
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
32
Copyright 2011 Pearson Education, Inc.
14) You intend to purchase your dream PC upon graduation in two years. It will have a cost of
$2,975, including all attachments and sales tax. You just received a $3,000 pre-graduation gift
from your rich uncle that you intend to deposit in a money market account that pays 6% interest,
compounded monthly. How much of your pre-graduation gift will you need to deposit in order to
have $2,975 available for the purchase of the PC upon graduation?
A) $1,275
B) $2,588
C) $2,975
D) $1,567
E) $2,639
Diff: 3
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value
Principles: Principle 1: Money Has a Time Value
15) Assume that two investments have a three-year life and generate the cash flows shown
below. Which of the two would you prefer?
Year
Investment A Investment B
1
$5,000
$8,000
2
$5,000
$5,000
3
$5,000
$2,000
A) Investment A, since it has the most even cash flows
B) Investment B, since it gives you the largest cash flows in earlier years
C) Neither, since they both have equal lives
D) Both investments are equally attractive
E) None of the above
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
33
Copyright 2011 Pearson Education, Inc.
16) You have just purchased an investment that generates the cash flows that are shown below.
You are able to invest your money at 5.75%, compounded annually. How much is this
investment worth today?
Year
Amount
0
$0
1
$1,250
2
$1,585
3
$1,750
4
$2,225
5
$3,450
A) $7,758
B) $4,521
C) $10,260
D) $8,467
E) $6,583
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
17) To evaluate and compare investment proposals, we must adjust all cash flows to a common
date.
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
18) Consider an investment that has cash flows of $500 the first year and $400 for the next four
years. If your opportunity cost is 10%, how much is this investment worth to you?
Answer: PV = $500(.909) = $454.50
PV = $400(3.170)(.909) = $1,152.61
454.50 + 1152.61 = $1,607.11
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
34
Copyright 2011 Pearson Education, Inc.
19) If your opportunity cost is 10%, how much are you willing to pay for an investment
promising $750 per year for the first four years and $450 for the next six years?
Answer: PV = $750(3.17) = $2,377.50
PV = $450(4.355)(.683) = $1,338.51
2377.50 + 1338.51 = $3,716.01
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
20) You have been offered the opportunity to invest in a project which will pay $1,000 per year
at the end of years one through 10 and $2,000 per year at the end of years 21 through 30. If the
appropriate discount rate is 8%, what is the present value of this cash flow pattern?
Answer: Present value of $1,000 per year for years 1 through 10 = $1,000(6.710) = $6,710 i =
8%
Value in year 20 of annuity of $2,000 per year for years 21 through 30 = $2,000(6.710) =
$13,420
Present value of annuity of $2,000 per year for years 21 through 30 = $13,420(.215) = $2,885.30
Total present value = $6,710 + $2,885.30 = $9,595.30
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
21) You are considering purchasing common stock in AMZ Corporation. You anticipate that the
company will pay dividends of $5.00 per share next year and $7.50 per share in the following
year. You also believe that you can sell the common stock two years from now for $30.00 per
share. If you require a 14% rate of return on this investment, what is the maximum price that you
would be willing to pay for a share of AMZ common stock?
Answer:
PV = $5.00 PVIF[14%, 1 yr] + ($7.50 + $30.00) PVIF[14%, 2 yr]
= $5.00(.877) + ($37.50)(.769)
= $33.22
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
35
Copyright 2011 Pearson Education, Inc.
22) You have decided to invest $500 in a mutual fund today and make $500 end-of-the-year
investments in the fund each year until you retire for 40 years. Assuming an opportunity cost of
12%, what do you estimate that you will have in this account at retirement?
Answer:
Calculator steps:
-500
PV
-500
PMT
40
N
12
I/yr or I
FV = $430,071
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
23) You are planning to deposit $10,000 today into a bank account. Five years from today you
expect to withdraw $7,500. If the account pays 5% interest per year, how much will remain in
the account eight years from today?
Answer:
FV = $10,000 FVIF[5%, 5 yr]
= $10,000(1.276) = $12,760
Amount to invest in remaining three years = $12,760 - $7,500 = $5,260
FV = $5,260 FVIF[5%, 3 yr]
= $5,260(1.158) = $6,091.08
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value complex income stream
Principles: Principle 1: Money Has a Time Value
24) Suppose you are 40 years old and plan to retire in exactly 20 years. 21 years from now you
will need to withdraw $5,000 per year from a retirement fund to supplement your social security
payments. You expect to live to the age of 85. How much money should you place in the
retirement fund each year for the next 20 years to reach your retirement goal if you can earn 12%
interest per year from the fund?
Answer: Amount in fund at age 60 = $5,000 PVIFA[12%, 25 yr]
= $5,000(7.843) = $39,215
$39,215 = (annual contribution) FVIFA[12%, 20 yr]
$39,215 = (annual contribution)(72.052)
Annual contribution = $39,215/72.052 = $544.26
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value complex income stream
Principles: Principle 1: Money Has a Time Value
36
Copyright 2011 Pearson Education, Inc.
25) An investment will pay $500 in three years, $700 in five years, and $1,000 in nine years. If
the opportunity rate is 6%, what is the present value of this investment?
Answer:
PV = $500(1/(1.06)3) + $700(1/1.06)5) + $1000(1/(1.06)9)
PV = $500(.840) + $700(.747) + $1000(.592)
= $420.00 + $522.90 + $592.00
= $1,534.90
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
26) What is the value (price) of a bond that pays $400 semiannually for 10 years and returns
$10,000 at the end of 10 years? The market discount rate is 10% paid semiannually.
Answer: Bond value =
= $400[12.462] + $10,000[.386]
= $4984.80 + $3,860 = $8,844.80
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
27) Delight Candy, Inc. is choosing between two bonds in which to invest their cash. One bond
is being offered from Hershey's and will mature in 10 years and pays 12% per year, compounded
quarterly. The other alternative is a Mars bond that will mature in 20 years and that pays 12% per
year, compounded quarterly. What would be the present value of each bond if the discount rate is
10%?
Answer:
Bond A
PV = $1,000, 10 years, 12% interest compounded quarterly, 10% discount rate
PV = $1,125.51
Bond B
PV = $1,000, 20 years, 12% interest compounded quarterly, 10% discount rate
PV = $1,172.26
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
37
Copyright 2011 Pearson Education, Inc.
28) In order to send your oldest child to law school when the time comes, you want to
accumulate $40,000 at the end of 18 years. Assuming that your savings account will pay 6%
compounded annually, how much would you have to deposit if:
a. you want to deposit an amount annually at the end of each year?
b. you want to deposit one large lump sum today?
Pymt = $1,294.26
b. Pymt = $14,013.75
Diff: 2
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value
Principles: Principle 1: Money Has a Time Value
38
Copyright 2011 Pearson Education, Inc.

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