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for possible end-of-year cash flows in each of the next three years:
Year 1 Year 2 Year 3
Prob Cash Flow Prob Cash Flow Prob Cash Flow
0.30 $300 0.15 $100 0.25 $200
0.40 500 0.35 200 0.75 800
0.30 700 0.35 600
0.15 900
Using an interest rate of 8 percent, find the expected present value of
these uncertain cash flows. (Hint: Find the expected cash flow in each
year, then evaluate those cash flows.)
a. $1,204.95
b. $ 835.42
c. $1,519.21
d. $1,580.00
e. $1,347.61
74. Foster Industries has a project that has the following cash flows:
Year Cash Flow
0 -$300.00
1 100.00
2 125.43
3 90.12
4 ?
What cash flow will the project have to generate in the fourth year in
order for the project to have a 15 percent rate of return?
a. $ 15.55
b. $ 58.95
c. $100.25
d. $103.10
e. $150.75
75. John Keene recently invested $2,566.70 in a project that is promising to
return 12 percent per year. The cash flows are expected to be as follows:
End of Year Cash Flow
1 $325
2 400
3 550
4 ?
5 750
6 800
What is the cash flow at the end of the 4th year?
a. $1,187
b. $ 600
c. $1,157
d. $ 655
e. $1,267
76. You recently purchased a 20-year investment that pays you $100 at t = 1,
$500 at t = 2, $750 at t = 3, and some fixed cash flow, X, at the end of
each of the remaining 17 years. You purchased the investment for
$5,544.87. Alternative investments of equal risk have a required return
of 9 percent. What is the annual cash flow received at the end of each
of the final 17 years, that is, what is X?
a. $600
b. $625
c. $650
d. $675
e. $700
77. A 10-year security generates cash flows of $2,000 a year at the end of
each of the next three years (t = 1, 2, and 3). After three years, the
security pays some constant cash flow at the end of each of the next six
years (t = 4, 5, 6, 7, 8, and 9). Ten years from now (t = 10) the
security will mature and pay $10,000. The security sells for $24,307.85
and has a yield to maturity of 7.3 percent. What annual cash flow does
the security pay for years 4 through 9?
a. $2,995
b. $3,568
c. $3,700
d. $3,970
e. $4,296
78. An investment costs $3,000 today and provides cash flows at the end of
each year for 20 years. The investment's expected return is 10 percent.
The projected cash flows for Years 1, 2, and 3 are $100, $200, and $300,
respectively. What is the annual cash flow received for each of Years 4
through 20 (17 years)? (Assume the same payment for each of these years.)
a. $285.41
b. $313.96
c. $379.89
d. $417.87
e. $459.66
79. If you buy a factory for $250,000 and the terms are 20 percent down, the
balance to be paid off over 30 years at a 12 percent rate of interest on
the unpaid balance, what are the 30 equal annual payments?
a. $20,593
b. $31,036
c. $24,829
d. $50,212
e. $ 6,667
80. You have just taken out an installment loan for $100,000. Assume that
the loan will be repaid in 12 equal monthly installments of $9,456 and
that the first payment will be due one month from today. How much of
your third monthly payment will go toward the repayment of principal?
a. $7,757.16
b. $6,359.12
c. $7,212.50
d. $7,925.88
e. $8,333.33
81. A homeowner just obtained a $90,000 mortgage. The mortgage is for 30
years (360 months) and has a fixed nominal annual rate of 9 percent, with
monthly payments. What percentage of the total payments made the first
two years will go toward payment of interest?
a. 89.30%
b. 91.70%
c. 92.59%
d. 93.65%
e. 94.76%
82. You recently obtained a $135,000, 30-year mortgage with a nominal
interest rate of 7.25 percent. Assume that payments are made at the end
of each month. What portion of the total payments made during the fourth
year will go towards the repayment of principal?
a. 9.70%
b. 15.86%
c. 13.75%
d. 12.85%
e. 14.69%
83. John and Peggy recently bought a house, and they financed it with a
$125,000, 30-year mortgage with a nominal interest rate of 7 percent.
Mortgage payments are made at the end of each month. What portion of
their mortgage payments during the first three years will go towards
repayment of principal?
a. 12.81%
b. 13.67%
c. 14.63%
d. 15.83%
e. 17.14%
84. The Taylor family has a $250,000 mortgage. The mortgage is for 15 years,
and has a nominal rate of 8 percent. Mortgage payments are due at the
end of each month. What percentage of the monthly payments during the
fifth year goes towards repayment of principal?
a. 46.60%
b. 43.16%
c. 57.11%
d. 19.32%
e. 56.84%
85. The Bunker Family recently entered into a 30-year mortgage for $300,000.
The mortgage has an 8 percent nominal interest rate. Interest is
compounded monthly, and all payments are due at the end of the month.
What will be the remaining balance on the mortgage after five years?
a. $ 14,790.43
b. $285,209.57
c. $300,000.00
d. $366,177.71
e. $298,980.02
86. Jamie and Jake each recently bought a different new car. Both received a
loan from a local bank. Both loans have a nominal interest rate of 12
percent with payments made at the end of each month, are fully
amortizing, and have the same monthly payment. Jamie's loan is for
$15,000; however, his loan matures at the end of 4 years (48 months),
while Jake's loan matures in 5 years (60 months). After 48 months
Jamie's loan will be paid off. At the end of 48 months what will be the
remaining balance on Jake's loan?
a. $ 1,998.63
b. $ 2,757.58
c. $ 3,138.52
d. $ 4,445.84
e. $11,198.55
87. If it were evaluated with an interest rate of 0 percent, a 10-year
regular annuity would have a present value of $3,755.50. If the future
(compounded) value of this annuity, evaluated at Year 10, is $5,440.22,
what effective annual interest rate must the analyst be using to find the
future value?
a. 7%
b. 8%
c. 9%
d. 10%
e. 11%
88. Steaks Galore needs to arrange financing for its expansion program. One
bank offers to lend the required $1,000,000 on a loan that requires
interest to be paid at the end of each quarter. The quoted rate is 10
percent, and the principal must be repaid at the end of the year. A
second lender offers 9 percent, daily compounding (365-day year), with
interest and principal due at the end of the year. What is the
difference in the effective annual rates (EFF%) charged by the two banks?
a. 0.31%
b. 0.53%
c. 0.75%
d. 0.96%
e. 1.25%
89. You have just taken out a 10-year, $12,000 loan to purchase a new car.
This loan is to be repaid in 120 equal end-of-month installments. If
each of the monthly installments is $150, what is the effective annual
interest rate on this car loan?
a. 6.5431%
b. 7.8942%
c. 8.6892%
d. 8.8869%
e. 9.0438%
90. Gilhart First National Bank offers an investment security with a 7.5
percent nominal annual return, compounded quarterly. Gilhart's
competitor, Olsen Savings and Loan, is offering a similar security that
bears the same risk and same effective rate of return. However, Olsen's
security pays interest monthly. What is the nominal annual return of the
security offered by Olsen?
a. 7.39%
b. 7.45%
c. 7.50%
d. 7.54%
e. 7.59%
91. You plan to invest $5,000 at the end of each of the next 10 years in an
account that has a 9 percent nominal rate with interest compounded
monthly. How much will be in your account at the end of the 10 years?
a. $ 75,965
b. $967,571
c. $ 84,616
d. $ 77,359
e. $ 80,631
92. You are willing to pay $15,625 to purchase a perpetuity that will pay you
and your heirs $1,250 each year, forever. If your required rate of
return does not change, how much would you be willing to pay if this were
a 20-year annual payment, ordinary annuity instead of a perpetuity?
a. $10,342
b. $11,931
c. $12,273
d. $13,922
e. $17,157
93. An investment pays you $5,000 at the end of each of the next five years.
Your plan is to invest the money in an account that pays 8 percent
interest, compounded monthly. How much will you have in the account
after receiving the final $5,000 payment in 5 years (60 months)?
a. $ 25,335.56
b. $ 29,508.98
c. $367,384.28
d. $304,969.90
e. $ 25,348.23
94. A baseball player is offered a 5-year contract that pays him the
following amounts:
Year 1: $1.2 million
Year 2: 1.6 million
Year 3: 2.0 million
Year 4: 2.4 million
Year 5: 2.8 million
Under the terms of the agreement all payments are made at the end of each
year.
Instead of accepting the contract, the baseball player asks his agent to
negotiate a contract that has a present value of $1 million more than
that which has been offered. Moreover, the player wants to receive his
payments in the form of a 5-year annuity due. All cash flows are
discounted at 10 percent. If the team were to agree to the player's
terms, what would be the player's annual salary (in millions of dollars)?
a. $1.500
b. $1.659
c. $1.989
d. $2.343
e. $2.500
95. Karen and her twin sister, Kathy, are celebrating their 30th birthday
today. Karen has been saving for her retirement ever since their 25th
birthday. On their 25th birthday, she made a $5,000 contribution to her
retirement account. Every year thereafter on their birthday, she has
added another $5,000 to the account. Her plan is to continue
contributing $5,000 every year on their birthday. Her 41st, and final,
$5,000 contribution will occur on their 65th birthday.
So far, Kathy has not saved anything for her retirement but she wants to
begin today. Kathy's plan is to also contribute a fixed amount every
year. Her first contribution will occur today, and her 36th, and final,
contribution will occur on their 65th birthday. Assume that both
investment accounts earn an annual return of 10 percent. How large does
Kathy's annual contribution have to be for her to have the same amount in
her account at age 65, as Karen will have in her account at age 65?
a. $9,000.00
b. $8,154.60
c. $7,398.08
d. $8,567.20
e. $7,933.83
96. Jim and Nancy just got married today. They want to start saving so they
can buy a house five years from today. The average house in their town
today sells for $120,000. Housing prices are expected to increase
3 percent a year. When they buy their house five years from now, Jim and
Nancy expect to get a 30-year (360-month) mortgage with a 7 percent
nominal interest rate. They want the monthly payment on their mortgage
to be $500 a month.
Jim and Nancy want to buy an average house in their town. They are
starting to save today for a down payment on the house. The down payment
plus the mortgage will equal the expected price of the house. Their plan
is to deposit $2,000 in a brokerage account today and then deposit a
fixed amount at the end of each of the next five years. Assuming that the
brokerage account has an annual return of 10 percent, how much do Jim and
Nancy need to deposit at the end of each year in order to accomplish
their goal?
a. $10,634
b. $ 9,044
c. $ 9,949
d. $ 9,421
e. $34,569
97. Today is your 25th birthday. Your goal is to have $2 million by the time
you retire at age 65. So far you have nothing saved, but you plan on
making the first contribution to your retirement account today. You plan
on making three other contributions to the account, one at age 30, age
35, and age 40. Since you expect that your income will increase rapidly
over the next several years, the amount that you contribute at age 30
will be double what you contribute today, the amount at age 35 will be
three times what you contribute today, and the amount at age 40 will be
four times what you contribute today. Assume that your investments will
produce an average annual return of 10 percent. Given your goal and
plan, what is the minimum amount you need to contribute to your account
today?
a. $10,145
b. $10,415
c. $10,700
d. $10,870
e. $11,160
98. Your lease calls for payments of $500 at the end of each month for the
next 12 months. Now your landlord offers you a new 1-year lease that
calls for zero rent for 3 months, then rental payments of $700 at the end
of each month for the next 9 months. You keep your money in a bank time
deposit that pays a nominal annual rate of 5 percent. By what amount
wo
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