41) How much money would you have to deposit today to create an income stream that pays $10,000 one
year from today and continues to make annual payments forever, with payments after the first $10,000
growing at 4% per year? Assume money that you invest today to fund this income stream earns a 7% rate
of return.
A) $142,857
B) $250,000
C) $1,250,000
D) $333,333
42) A certain investment promises to pay you $2,500 per year forever with the first payment starting next
year. If you can earn a 5% return on similar investments, what’s the most you would pay for this
investment today?
A) $50,000
B) $5,000
C) $41,667
D) $62,500
43) A perpetuity will pay you $100 starting next year and continuing at that level forever. The
appropriate discount rate for the perpetuity is 10%. Calculate the present value of (1) the infinite stream
of payments, i.e., the entire perpetuity, and (2) the first 20 payments. Compare these two present values
and comment on what they can tell you about the present value of the perpetuity’s payments in the very
distant future (i.e., payments made later than 20 years in the future).
44) You inherited an investment portfolio worth $1 million. The portfolio earns a return of 9% per year.
You want to withdraw money from this portfolio once per year starting one year from today, and you
want to continue making withdrawals forever. Furthermore, you want to increase your withdrawals at
3% per year to keep up with inflation. How large can your first withdrawal be?
45) A certain investment promises to pay you $2,500 per year forever with the first payment starting 5
years from now. If you can earn a 5% return on similar investments, what’s the most you would pay for
this investment today?
A) $50,000
B) $39,176
C) $41,135
D) $37,311
46) Ashley is planning to attend college when she graduates from high school 7 years from now. She
anticipates that she will need $20,000 at the beginning of each of the four college years to pay for tuition
and fees, and have some spending money (i.e., she needs to be able to withdraw $20,000 from savings
four times, with the first withdrawal taking place 7 years from now). Ashley’s father has promised to help
her save for college by making 7 deposits of $7,000 each into an investment accounting earning 8 percent
interest. His first payment comes a year from today. Will there be enough money in the account for
Ashley to pay for her college expenses? Assume the rate of interest stays at 8 percent during the college
years.
5.4 Mixed streams
1) You receive $100 today, $200 in one year, and $300 in two years. If you deposit these cash flows into an
account earning 12 percent, the value in the account three years from now is ________.
A) less than $600
B) $649
C) $727
D) $815
2) You receive $1,200 today, $2,200 in one year, and $3,300 in two years. If you deposit these cash flows in
an account earning 12%, how much money is in the account three years from now?
A) $6,221
B) $5,554
C) $7,269
D) $8,142
3) Find the future value at the end of year 3 of the following stream of cash flows received at the end of
each year, assuming the firm can earn 17 percent on its investments.
A) $16,320
B) $20,127
C) $23,548
D) $27,551
4) Find the future value at the end of year 3 of the following stream of cash flows received at the end of
each year, assuming the firm can earn 8 percent on its investments.
A) $51,780
B) $39,248
C) $47,944
D) $40,981
5) You receive $1,000 in 1 year, $1,200 in 2 years, and $1,300 in 3 years. The present value today of these
future receipts is ________ if the opportunity cost is 7 percent.
A) $2,500
B) $3,044
C) $4,036
D) $3,257
6) You will receive $100 in 1 year, $200 in 2 years, and $300 in 3 years. If you can earn 13% on your
investments, the present value of these future receipts is ________.
A) $453
B) $512
C) $801
D) $600
7) Find the present value of the following stream of cash flows assuming an opportunity cost of 14
percent.
A) $59,169
B) $92,443
C) $81,090
D) $51,903
8) Find the present value of the following stream of cash flows assuming an opportunity cost of 25
percent.
A) $27,168
B) $33,960
C) $72,656
D) $41,674
9) Find the present value of the following stream of cash flows assuming an opportunity cost of 9 percent.
A) $85,791
B) $187,838
C) $65,213
D) $79,345
10) Find the present value of the following stream of a firm’s cash flows, assuming that the firm’s
opportunity cost is 14 percent.
A) $131,068
B) $149,417
C) $485,897
D) $104,322
11) During her four years at college, Hayley received the following amounts of money at the end of each
year from her grandmother. She deposited her money in a savings account paying 6 percent rate of
interest. How much money will Hayley have on graduation day?
12) You have provided your friend with a service worth $8,500. Your friend offers you the following
sequence of end–of-year cash flows instead of paying $8,500 today. Should you accept his offer if your
opportunity cost is 8 percent?
13) Calculate the present value of $5,800 received at the end of year 1, $6,400 received at the end of year 2,
and $8,700 at the end of year 3, assuming an opportunity cost of 13 percent.
14) Calculate the present value of $800 received at the beginning of year 1, $400 received at the beginning
of year 2, and $700 received at the beginning of year 3, assuming an opportunity cost of 9 percent.
15) Calculate the combined future value at the end of year 3 of $1,000 received at the end of year 1, $3,000
received at the end of year 2, and $5,000 received at the end of year 3, all sums deposited at 5 percent.
16) You are considering the purchase of new equipment for your company and you have narrowed down
the possibilities to two models which perform equally well. However, the method of paying for the two
models is different. Model A requires $5,000 per year payment for the next five years. Model B requires
the following payment schedule. Which model should you buy if your opportunity cost is 8 percent?
17) Last Christmas, Danny received an annual bonus of $1,500. These annual bonuses are expected to
grow by 5 percent for the next 5 years. How much will Danny have at the end of the fifth year if he
invests his Christmas bonuses (including the most recent bonus) in an account paying 8 percent per year?
18) Calculate the present value of the following stream of cash flows, assuming that the firm’s
opportunity cost is 15 percent.
5.5 Compounding interest more frequently than annually
1) The nominal (stated) annual rate is the rate of interest actually paid or earned.
2) The nominal and effective rates are equivalent for annual compounding.
3) The effective annual rate increases with increasing compounding frequency.
4) The annual percentage rate (APR) is the nominal rate of interest, found by multiplying the periodic rate
by the number of periods in one year.
5) The annual percentage yield (APY) is the effective rate of interest that must be disclosed to customers
by banks on their savings products as a result of “truth in savings laws.”
6) The effective rate of interest is the contractual rate of interest charged by a lender or promised by a
borrower.
7) The effective rate of interest differs from the nominal rate of interest in that it reflects the impact of
compounding frequency.
8) For any interest rate and for any period of time, the more frequently interest is compounded, the
greater the amount of money that has to be invested today in order to accumulate a given future amount.
9) The effective rate of interest and compounding frequency are inversely related.
10) The rate of interest agreed upon contractually charged by a lender or promised by a borrower is the
________ interest rate.
A) effective
B) nominal
C) discounted
D) continuous
11) The rate of interest actually paid or earned, also called the annual percentage rate (APR), is the
________ interest rate.
A) effective
B) nominal
C) discounted
D) continuous
12) The future value of $200 received today and deposited at 8 percent compounded semiannually for
three years is ________.
A) $380
B) $158
C) $253
D) $252
13) The future value of $100 received today and deposited in an account for four years paying semiannual
interest of 6 percent is ________.
A) $450
B) $127
C) $889
D) $134
14) The future value of $200 received today and deposited for three years in an account which pays
semiannual interest of 8 percent is ________.
A) $253.00
B) $252.00
C) $158.00
D) $134.66
15) The future value of an annuity of $1,000 each quarter for 10 years, deposited at 12 percent
compounded quarterly is ________.
A) $17,549
B) $75,401
C) $93,049
D) $11,200
16) What is the highest effective rate attainable with a 12 percent nominal rate?
A) 12.00%
B) 12.55%
C) 12.75%
D) 12.95%
17) Gina has planned to start her college education four years from now. To pay for her college education,
she has decided to save $1,000 a quarter for the next four years in an investment account paying 12
percent interest. How much will she have at the end of the fourth year?
A) $1,574
B) $19,116
C) $20,157
D) $16,000
18) How much would Sophie have in her account at the end of 10 years if she deposit $2,000 into the
account today if she earned 8 percent interest and interest is compounded continuously?
A) $4,317
B) $4,134
C) $4,451
D) $4,521
19) Assume Julian has a choice between two deposit accounts. Account A has an annual percentage rate
of 7.55 percent but with interest compounded monthly. Account B has an annual percentage rate of 7.45
percent with interest compounded continuously. Which account provides the highest effective annual
return?
A) Account A
B) Account B
C) Both provide the same effective annual return.
D) We don’t have sufficient information to make a choice.
20) Calculate the future value of $6,490 received today and deposited for five years in an account which
pays interest of 14 percent compounded semiannually.
21) Calculate the future value of $10,000 received today and deposited for six years in an account which
pays interest of 12 percent compounded quarterly.
22) Jeanne has just graduated from high school and has received an award for $5,000. She would like to
deposit the money in an interest earning account until she graduates from college (i.e., four years from
now). In her search for the highest interest earning account, she has narrowed the list down to the
following two accounts: 1) bank A pays 9 percent interest compounded annually, and 2) bank B pays 8
percent interest compounded semiannually. Which is the better offer, and how much will Jeanne have
upon graduation from college?
23) Assume you have a choice between two deposit accounts. Account X has an annual percentage rate of
12.25 percent but with interest compounded monthly. Account Y has an annual percentage rate of 12.20
percent with interest compounded continuously. Which account provides the highest effective annual
return?
24) Carlos is the new assistant branch manager of a larger Florida–based bank and the branch manager
has asked him a question to test his knowledge. The question is which rate should the bank advertise on
monthly-compounded loans, the nominal annual percentage rate or the effective annual percentage rate?
Which rate should the bank advertise on quarterly-compounded savings accounts? Explain. As a
consumer, which would you prefer to see and why?
5.6 Special applications of time value
1) In general, with an amortized loan, the payment amount remains constant over the life of the loan, the
principal portion of each payment grows over the life of the loan, and the interest portion of each
payment declines over the life of the loan.
2) In general, with an amortized loan, the payment amount remains constant over the life of the loan, the
principal portion of each payment declines over the life of the loan, and the interest portion of each
payment grows over the life of the loan.
3) In general, with an amortized loan, the payment amount remains constant over the life of the loan,
both the principal portion of and the interest portion declines over the life of the loan.
4) In general, with an amortized loan, the payment amount grows over the life of the loan, the principal
portion of each payment grows over the life of the loan, and the interest portion declines over the life of
the loan.
5) When computing an interest or growth rate, the rate will increase with an increase in future value,
holding present value and the number of periods constant.
6) When computing an interest or growth rate, the rate will decrease with an increase in future value,
holding present value and the number of periods constant.
7) When computing an interest or growth rate, the rate will increase with a decrease in future value,
holding present value and the number of periods constant.
8) When computing the number of deposits needed to accumulate to a future sum, it will take longer if
the interest rate decreases, holding the future value and deposit size constant.
9) When computing the number of deposits needed to accumulate a future sum, it will take longer if the
interest rates are higher, holding the future value and deposit size constant.
10) The time value concept/calculation used in amortizing a loan is ________.
A) future value of a dollar
B) future value of an annuity
C) present value of a dollar
D) present value of an annuity
11) If a United States Savings bond can be purchased for $29.50 and has a maturity value of $100 at the
end of 25 years, what is the annual rate of return on the bond?
A) 5 percent
B) 6 percent
C) 7 percent
D) 8 percent
12) If a United States Savings bond can be purchased for $14.60 and has a maturity value at the end of 25
years of $100, what is the annual rate of return on the bond?
A) 6 percent
B) 7 percent
C) 8 percent
D) 9 percent