51) Congratulations! You have been accepted to study gourmet cooking at the Cordon-Bleu
Cooking School in Paris. You will need $10,000 every 6 months (beginning today) for the next
three years to cover tuition and living expenses. Mom and Dad have agreed to pay for your
education, and want to make one deposit today in a bank account earning 6% interest,
compounded semi-annually. How much must they deposit now so that you can withdraw
$10,000 at the beginning of each semester over the next 3 years?
A) $54,172
B) $55,797
C) $57,422
D) $56,604
52) You are thinking of buying a craft emporium. It is expected to generate cash flows of
$30,000 per year in years 1 through 5, and $40,000 per year in years 6 through 10. If the
appropriate discount rate is 8%, what amount are you willing to pay for the emporium?
A) $135,288
B) $167,943
C) $215,048
D) $228,476
53) You have contracted to buy a house for $250,000, paying $30,000 down and taking out a
fully amortizing loan for the balance, at a 5.7% annual rate for 30 years. What will your monthly
payment be if they make equal monthly installments over the next 30 years (to the nearest
dollar)?
A) $1,035
B) $1,123
C) $1,189
D) $1,277
54) You bought a racehorse that has had a winning streak for four years, bringing in $500,000 at
the end of each year before dying of a heart attack. If you paid $1,518,675 for the horse 4 years
ago, what was your annual return over this 4-year period?
A) 8%
B) 33%
C) 18%
D) 12%
55) Jimmy just bought a new Ford SUV for his business. The price of the vehicle was $40,000.
Jimmy made a $5,000 down payment and took out an amortized loan for the rest. The car
dealership made the loan at 8% interest compounded monthly for five years. He is to pay back
the principal and interest in equal monthly installments beginning one month from now.
Determine the amount of Jimmy’s monthly payment.
A) $634.56
B) $709.67
C) $745.87
D) $809.33
56) You just graduated and landed your first job in your new career. You remember that your
favorite finance professor told you to begin the painless job of saving for retirement as soon as
possible, so you decided to put away $2,000 at the end of each year in a Roth IRA. Your
expected annual rate of return on the IRA is 7.5%. How much will you accumulate at retirement
after 40 years of investing (note: this may assume that you are even retiring early)?
A) $94,426
B) $247,921
C) $1,088,632
D) $454,513
57) Congratulations! You are the proud winner of the multi-state Sour Ball Lottery. You are to
receive $2,000,000 at the end of each year for the next 20 years. While the Lottery Commission
refers to this as a $40,000,000 jackpot, if you choose the “cash option” they will give you much
less than that; you can receive a lump sum payment today equal to the present value of the
ordinary annuity instead of the 20 annual payments. If the discount rate that the Lottery
Commission uses to determine the lump sum payoff is 7%, what is your payoff if you select the
cash option?
A) $26,945,332
B) $39,707,503
C) $42,977,401
D) $21,188,028
58) You are ready to retire. A glance at your 401(k) statement indicates that you have $750,000.
If the funds remain in an account earning 9.0%, how much could you withdraw at the beginning
of each year for the next 25 years?
A) $55,620
B) $70,050
C) $35,830
D) $2,500
59) How much would you be willing to pay (rounded to the nearest dollar) for a 20-year annuity
due if the payments are $4,500 per year and you want to earn a rate of return equal to 5.5% per
year?
A) $84,500
B) $63,445
C) $56,734
D) $53,777
60) How much would you be willing to pay (rounded to the nearest dollar) for a 20-year ordinary
annuity if the payments are $4,500 per year and you want to earn a rate of return equal to 5.5%
per year?
A) $84,500
B) $63,445
C) $56,734
D) $53,777
61) Your son will be attending an expensive university in 12 years. You deposit $5,000 per year
for 12 years, beginning today. How much money will be in the college fund 12 years from now
if the fund earns 8% per year?
62) If you wish to accumulate $200,000 in the child’s college fund after 18 years, and can invest
at a 7.5% annual rate, how much must you invest at the end of each year if the first deposit is
made at the end of the first year?
63) Betty borrows $60,000 at 12 percent compounded annually. The loan is to be repaid in five
equal annual end-of-year installments. How much must each loan payment be?
64) You are currently 25 years of age. You have developed a lifetime budget that includes
$50,000 at age 40 for a college fund for your kids and $25,000 per year for 20 years to
supplement your retirement, the first payment on your 60th birthday and the last payment on
your 79th birthday. You open an investment account on your 25th birthday that promises to pay
9% interest compounded annually. You want to deposit equal annual amounts into the account
every year on your birthday, starting today (your 25th birthday) and continuing until you are 40
years old (i.e., the last deposit is made on your 40th birthday). How much will each deposit have
to be if you want to meet your financial goals?
65) Bob invested $2,000 in an investment fund on his 21st birthday. The fund pays 7% interest
compounded semiannually. Bob is celebrating his 50th birthday today. Bob decides he wants to
retire on his 60th birthday and he wants to withdraw $75,000 per year, the first withdrawal on his
60th birthday and the last withdrawal on his 90th birthday. Bob expects to receive $100,000
from his employer on his 55th birthday in recognition of his long service to the company.
Assume Bob has not taken any money out of his investment fund since he initially funded it on
his 21st birthday, and that he will deposit the $100,000 from his employer into the investment
fund on his 55th birthday. The investment fund will be used to pay for Bob’s retirement.
If Bob makes no additional deposits into his investment fund, how much will be available for
retirement at age 60?
Since the amount in (a) is insufficient to meet his retirement goals, Bob decides to deposit equal
annual amounts into the investment fund beginning on his 51st birthday and ending on his 59th
birthday, so that he can meet his retirement goals. How much will each deposit be?
66) Bill starts a retirement fund at age 21 and plans on depositing equal annual amounts on each
birthday, starting at age 21, and ending at age 60. He wants to have $2 million at age 60. John
starts his fund on his 30th birthday. He wants to deposit equal annual amounts on each birthday
starting on his 30th birthday and ending on his 60th birthday. John wants to have $2 million at
age 60. If the investment funds earn 10% per year, calculate the amounts the Bill and John
respectively will have to save each year (rounded to the nearest dollar) to meet their goals.
Comment on the difference.
67) An investment promises to pay you the following amounts at the end of each of the next 10
years: (1) $1,000, (2) $2,000, (3) $3,000, (4) $4,000, (5) – (10) $5,000 per year. If you want to
earn a return of 8% per year, how much will you be willing to pay for the investment today?
68) You borrow $25,000 to buy a car, and agree to make 48 monthly payments of $607.39 to
repay the loan. What annual rate of interest, which is being compounded monthly, are you being
charged?
69) You wish to accumulate $10,000 by depositing $481.46 per month into a savings account
that earns 4.75% compounded monthly. How many monthly deposits must you make?
70) Today is your 30th birthday and you must choose between two retirement options. The first
option will provide you with 10 equal annual payments of $100,000 beginning on your 65th
birthday. The second option will provide you with one payment of $1,000,000 on your 70th
birthday. If the interest rate is 6 percent per year and you are assured of living to at least 80
years of age, which option is better?
71) A bond will pay $5,000 at maturity in 9 years. It also makes semi-annual interest payments
of $400 until maturity. If the discount rate is 7% compounded semi-annually, what should be the
market price of the bond?
72) Frank Zanca is considering three different investments that his broker has offered to him.
The different cash flows are as follows:
End of Year
A
B
C
1
300
400
2
300
3
300
4
300
300
600
5
300
6
300
7
300
8
300
600
Because Frank only has enough savings for one investment, his broker has proposed the third
alternative to be, according to his expertise, “the best in town.” However, Frank questions his
broker and wants to calculate the present value of each investment. Assuming a 15% discount
rate, what is Frank’s best alternative?
73) Leigh Delight Candy, Inc. is choosing between two bonds in which to invest their cash. One
is being offered from Hershey’s and will mature in 10 years and pay $30 each quarter. The other
alternative is a Mars’ bond that will mature in 20 years and pay $30 each quarter. What would be
the present value of each bond if the discount rate is 10% compounded quarterly, and each bond
pays $1,000 at maturity?
74) In order to send your first 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 equal amount at the end of each year?
b. You want to deposit one large lump sum today?
75) Cindy wants $2.5 million for her retirement at age 65. Cindy is 25 years old today and plans
to deposit equal amounts each year starting on her 26th birthday and ending on her 65th birthday.
If her investments earn 6% per year, how much must each deposit be?
76) A retirement home in Florida costs $200,000 today. Housing prices in Florida are increasing
at a rate of 4% per year. Joe wants to buy the home in 8 years when he retires. Joe has $25,000
right now in a savings account paying 8% interest per year. Joe wants to make eight equal
annual deposits into the savings account starting today. How much must each deposit be so Joe
will have enough money in his savings account to buy the retirement home when he retires?
5.4 Learning Objective 4
1) A return of 12% compounded annually is the same as a return of 1% per month.
2) The price of a computer today is $400 and inflation is 5% per year. Therefore, in two years the
price of the computer is expected to be $440.
3) If we invest money for 10 years at 8 percent interest, compounded semi-annually, we are
really investing money for 20 six-month periods, and receiving 4 percent interest each period.
4) For a given stated interest rate, an investor would receive a greater future value with daily
compounding as opposed to monthly compounding.
5) A certificate of deposit that pays 9.8% compounded monthly is better than a similar certificate
of deposit that pays 10% compounded only once per year.
6) A compound annuity involves depositing or investing a single sum of money and allowing it
to compound for a certain number of years.
7) Tim invested $1,000 in a mutual fund paying 8% per year. John invested $500 in the same
fund. If both Tim and John keep their money invested for the same period of time, Tim will end
up with twice as much money as John.
8) It is never appropriate to compare nominal rates unless they include the same number of
compounding periods per year.
9) Which of the following investments has the highest effective annual return (EAR)? (Assume
that all CDs are of equal risk.)
A) A bank CD that pays 7.00 percent interest compounded daily.
B) A bank CD that pays 7.10 percent compounded monthly.
C) A bank CD that pays 7.30 percent annually.
D) A bank CD that pays 7.25 percent compounded semiannually.
10) One bank offers you 4% interest compounded semiannually. What is the equivalent rate if
interest is compounded quarterly?
A) 3.98%
B) 3.96%
C) 3.92%
D) 1.00%
11) A financial analyst tells you that investing in stocks will allow you to double your money in
7 years. What annual rate of return is the analyst assuming you can earn?
A) 8.76%
B) 9.87%
C) 10.01%
D) 10.41%
12) You believe in the power of compounding and decide to save $1 per day by avoiding the
purchase of a soda. You deposit the $1 at the end of each day in a bank account that pays 8%
interest compounded daily. You are going to take a trip in 20 years with the money you have
accumulated. How much money will you have in 20 years, assuming 365 days per year?
A) $7,500
B) $12,438
C) $18,032
D) $22,456
13) Today is your 21st birthday and your bank account balance is $25,000. Your account is
earning 6.5% interest compounded semiannually. How much will be in the account on your 50th
birthday?
A) $159,795
B) $162,183
C) $163,823
D) $164,631
14) Today is your 21st birthday and your bank account balance is $25,000. Your account is
earning 6.5% interest compounded quarterly. How much will be in the account on your 50th
birthday?
A) $159,795
B) $162,183
C) $163,832
D) $164,631
15) Today is your 21st birthday and your bank account balance is $25,000. Your account is
earning 6.5% interest compounded monthly. How much will be in the account on your 50th
birthday?
A) $159,795
B) $162,183
C) $163,823
D) $164,631
16) Today is your 21st birthday and your bank account balance is $25,000. Your account is
earning 6.5% interest compounded daily. How much will be in the account on your 50th
birthday?
A) $159,795
B) $162,183
C) $163,823
D) $164,631
17) Your daughter is born today and you want her to be a millionaire by the time she is 35 years
old. open an investment account that promises to pay 12% per year. How much money must you
deposit today so your daughter will have $1,000,000 by her 35th birthday?
A) $28,571
B) $22,095
C) $20,045
D) $18,940
18) Your son is born today and you want to make him a millionaire by the time he is 50 years
old. You deposit $50,000 in an investment account and want to know what annual interest rate
must you earn in order to have the account value equal to $1,000,000 on your son’s 50th
birthday.
A) 17.8%
B) 12.4%
C) 9.5%
D) 6.2%
19) At 6 percent compounded monthly, how long will it take to triple your money?
A) 221 months
B) 175 months
C) 102 months
D) 48 months
20) If you invest $750 every six months at 8 percent 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
21) You are currently earning 12% compounded semiannually. Your investment company is
switching all accounts to daily compounding. What rate will give you the same effective annual
rate of return as you are receiving now?
A) 10.83%
B) 10.97%
C) 11.66%
D) 11.89%
22) What is the future value of $500 invested at 9.5% compounded quarterly for 12.5 years
(round to nearest $1)?
A) $670
B) $1,510
C) $1,617
D) $46,739
23) If you put $2,000 in a savings account that yields 8% compounded semi-annually, how much
money will you have in the account in 20 years (round to nearest $10)?
A) $6,789
B) $8,342
C) $9,602
D) $9,972
24) If you put $10,000 in an investment that returns 11 percent compounded monthly what
would you have after 10 years (round to nearest $1)?
A) $29,892
B) $27,559
C) $25,486
D) $22,489
25) If you want to have $5,000 in 10 years, how much money must you put in a savings account
today? (Assume that the savings account pays 4% and it is compounded daily; round to the
nearest $1).
A) $3,352
B) $3,370
C) $4,102
D) $4,207
26) You want $20,000 in 5 years to take your spouse on a second honeymoon. Your investment
account earns 7% compounded semiannually. How much money must you put in the investment
account today? (round to the nearest $1).
A) $14,178
B) $12,367
C) $15,985
D) $13,349
27) If you want to have $4,200 in 29 months, how much money must you put in a savings
account today? Assume that the savings account pays 12% and it is compounded monthly (round
to nearest $1).
A) $3,147
B) $3,009
C) $2,678
D) $2,439
28) If you want to have 1$2,500 in 57 months, how much money must you put in a savings
account today? Assume that the savings account pays 4.5% and it is compounded quarterly
(round to nearest $1).
A) $8,459
B) $10,106
C) $10,387
D) $11,129
29) If Cindy deposits $12,000 into a bank account that pays 6% interest compounded semi-
annually, what will the account balance be in seven years?
A) 18,151
B) 14,356
C) 16,987
D) 15,555
30) If Cathy deposits $12,000 into a bank account that pays 6% interest compounded quarterly,
what will the account balance be in seven years?
A) 18,001
B) 18,207
C) 19,112
D) 19,344
31) To compound $100 quarterly for 20 years at 8%, we must use
A) 40 periods at 4%.
B) 5 periods at 12%.
C) 10 periods at 4%.
D) 80 periods at 2%.
32) Cary’s wonderful parents established a college savings plan for him when he was born. They
deposited $50 into the account on the last day of each month. The account has earned 10%
compounded monthly, tax-free. How much can they withdraw on his 18th birthday to spend on
his education?
A) $27,360
B) $30,028
C) $33,407
D) $43,630
33) Cary’s wonderful parents established a college savings plan for him when he was born. They
deposited $50 into the account on the last day of each month. The account has earned 10%
compounded monthly, tax-free. Now he’s off to State U. What equal amount can they withdraw
beginning today (his 18th birthday) and each year for three additional years to spend on his
education, assuming that the account now earns 7% annually.
A) $8,285
B) $8,865
C) $9,486
D) $30,028
34) You discover an antique in your attic that you purchased at an estate sale 10 years ago for
$400. You auction it on Ebay and receive $8,000 for your item. What annual rate of return did
you earn?
A) 200.00%
B) 34.93%
C) 30.47%
D) 20.00%
35) Last National Bank is offering you a loan at 10%; payments on the loan are to be made
monthly. Credit Onion is offering you a loan where payments are to be made semi-annually; the
rate on the loan is also 10%. Local Bank down the street is also offering a loan at 10% where the
payments are made quarterly. Which loan has the lowest annual cost?
A) Last National Bank’s loan
B) Local Bank’s loan
C) Credit Onion’s loan
D) All of the loans will have the same annual cost.
36) You have $25,000 in an investment account today. How much will be in the account in 30
years if the account earns (a) 8% per year, (b) 8% compounded semiannually, (c) 8%
compounded quarterly, (d) 8% compounded monthly, and (e) 8% compounded daily? Comment
on the effect of more frequent compounding.
5.5 Learning Objective 5
1) A share of preferred stock that pays the same annual dividend forever is an example of a
perpetuity.
2) The present value of a $100 perpetuity discounted at 5% is $5,000.
3) You won the lottery and can receive either (1) $60,000 today, or (2) $10,000 one year from
today plus $25,000 two years from today plus $35,000 three years from today. You plan to use
the money to pay for your child’s college education in 15 years. You should
A) take the $60,000 today because of the time value of money regardless of current interest rates.
B) take option two because you get $70,000 rather than $60,000 regardless of current interest
rates.
C) take the $60,000 today only if the current interest rate is at least 16.67%
D) take the $60,000 today if you can earn 6.81% per year or more on your investments
4) You have a savings bond that will be worth $500 when it matures in 3 years, but you need
cash today. If the current going rate of interest is 5%, what is your bond worth if you sell it
today (rounded to the nearest dollar)?
A) $475
B) $432
C) $425
D) $412
5) A bond maturing in 10 years pays $80 each year (including year 10) and $1,000 upon
maturity. Assuming 10 percent to be the appropriate discount rate, the present value of the bond
is:
A) $877.11.
B) $1,000.00.
C) $416.39.
D) $1,785.67.
6) 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) 0.055
B) 0.010
C) 0.110
D) 0.220
7) What is the value on 1/1/10 of the following cash flows:
Date Cash Received Amount of Cash
1/1/11 $14,000
1/1/12 $20,000
1/1/13 $30,000
1/1/14 $43,000
1/1/15 $57,000
Use a 7% discount rate, and round your answer to the nearest $10.
A) $153,270
B) $128,490
C) $112,350
D) $107,330
8) A bond matures in 20 years, at which time it pays the owner $1,000. It also pays $70 at the
end of each of the next 20 years. If similar bonds are currently yielding 8%, what is the market
value of the bond?
A) over $1,000
B) under $1,000
C) exactly $1,000
D) cannot be determined from the information given
9) 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) $864
C) $885
D) $900
10) 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
11) You invest $1,000 at a variable rate of interest. Initially the rate is 4% compounded annually
for the first year, and the rate increases one-half of one percent annually for five years (year two’s
rate is 4.5%, year three’s rate is 5.0%, etc.). How much will you have in the account after five
years?
A) $1,276
B) $1,359
C) $1,462
D) $1,338
12) An investment will pay $500 in three years, $700 in five years and $1000 in nine years. If
your opportunity rate is 6%, what is the present value of this investment?
13) What is the present value of the following perpetuities?
a. $200 per year discounted at 6% annually
b. $500 per year discounted at 9% annually
c. $1,000 per year discounted at 5% annually
d. $550 per year discounted at 8% annually