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Financial Management: Core Concepts, 4e (Brooks)
Chapter 3 The Time Value of Money (Part 1)
1) Your grandmother places $13,000 into an account earning an interest rate of 7% per year.
After 5 years the account will be valued at $18,233.17. Which of the following statements is
CORRECT?
A) The present value is $13,000, the time period is 7 years, the present value is $18,233.17, and
the interest rate is 5%.
B) The future value is $13,000, the time period is 5 years, the principal is $18,233.17, and the
interest rate is 7%.
C) The principal is $13,000, the time period is 5 years, the future value is $18,233.17, and the
interest rate is 7%.
D) The principal is $13,000, the time period is 7 years, the future value is $18,233.17, and the
interest rate is 5%.
2) The one-time payment of money at a future date is often called a ________.
A) lump-sum payment
B) present value
C) principal amount
D) perpetuity payment
3) A $200 deposit today that earns an annual interest rate of 5% is worth how much at the end of
two years? Assume all interest received at the end of the first year is reinvested the second year.
A) $181.41
B) $220.00
C) $220.50
D) $242
4) An investment of $100 today is worth $116.64 at the end of two years if it earns an annual
interest rate of 8%. How much interest is earned in the first year and how much in the second
year of this investment?
A) The interest earned in year one is $8.32 and the interest earned in year two is $8.32.
B) The interest earned in year one is $8.00 and the interest earned in year two is $8.64.
C) The interest earned in year one is $8.64 and the interest earned in year two is $8.00.
D) There is not enough information to solve this problem.
5) ________ is simply the interest earned in subsequent periods on the interest earned in prior
periods.
A) Quoted interest
B) Anticipated interest
C) Simple interest
D) Compound interest
6) Which of the following is the CORRECT formula for calculating the future value?
A) FV =
B) FV = PV × (1 + r)n
C) PV = FV × (1 + r)n
D) PV = - 1
7) Which of the following will result in a future value greater than $100?
A) PV = $50, r = an annual interest rate of 10%, and n = 8 years.
B) PV = $75, r = an annual interest rate of 12%, and n = 3 years.
C) PV = $90, r = an annual interest rate of 14%, and n = 1 year.
D) All of the future values are greater than $100.
8) A two-year investment of $300 is made today at an annual interest rate of 4%. Which of the
following statements is TRUE?
A) The PV is $277.37.
B) The FV is $224.72.
C) The FV is $324.48.
D) This question is irrelevant because there are no two-year investments that earn an average of
4% per year.
9) A two-year investment of $200 is made today at an annual interest rate of 6%. Which of the
following statements is TRUE?
A) The interest earned in year two is $12.00 and year one is $12.72.
B) The interest earned in year one is $12.00 and year two is $12.72.
C) The FV is $224.00.
D) The future value would be greater if the interest rate were lower.
10) A two-year investment of $3500 is made today at an annual interest rate of 5.75%. Which of
the following statements is TRUE?
A) The future value would be greater if the interest rate was higher.
B) The present value would be greater if the interest rate was higher.
C) The future value would be greater if the interest rate was lower.
D) The future value does not change as the interest rate changes.
11) In two years Brandon plans to enroll at Umpqua University, a prestigious university in the
Pacific Northwest of the USA. If the current tuition is $23,500 per year and is expected to
increase at a rate of 6% per year, how much will Brandon pay in tuition his first year of school?
(His first tuition payment is exactly two years from today.) In his fourth year? (His last tuition
payment is exactly 5 years from today) (Rounded to the nearest dollar.)
A) $23,500 and $29,668
B) $26,405 and $29,668
C) $23,500 and $31,448
D) $26,405 and $31,448
12) Andy would like to buy a new car but must complete a two-year commitment to the Peace
Corp before he will drive the new car. The current price of the car Andy wants to buy is $32,000,
and the dealer expects the price of a similar new car to be $35,000 in two years. If Andy can earn
an annual interest rate of 4% on his money, should he buy the car now or wait for two years?
Why? Note: Storage costs if Andy purchases the car are $0. Please limit your considerations to
the factors offered in the answer choices.
A) Buy now because if Andy invests the $32,000 today it will only increase in value to $34,611,
and this is less than the cost of his desired new car in two years.
B) Andy is indifferent because his $32,000 investment will be worth exactly $35,000 after two
years.
C) Buy in two years because at $35,000 the car will cost less than the $36,385 Andy will have
after investing the money for two years.
D) Buy in two years because $35,000 is a "real deal" for the car Andy wants.
13) Susan and her spouse have saved $5,500 for a 12-day cruise vacation in Europe. The couple
needs $6,500 for a "nice" cabin or $7,000 for a "luxury" cabin. If cabin prices are expected to
remain constant for the next three years and Susan expects to earn 5% per year on her
investments, will the couple's savings be enough to afford the "nice" cabin in three years? Can
they afford the luxury cabin? Why or why not?
A) Yes, they can afford the "nice" cabin or the luxury cabin because their $5,500 investment will
increase to $6,367 by the end of year three.
B) Yes, they can afford the "nice" cabin or the luxury cabin because their $5,500 investment will
increase to $7,082 by the end of year three.
C) Yes, they can afford the "nice" cabin but NOT the luxury cabin because their $5,500
investment will only increase to $6,482 by the end of year three.
D) No, they cannot afford the "nice" cabin or the luxury cabin because their $5,500 investment
will only increase to $6,367 by the end of year three.
14) A home improvement firm has quoted a price of $14,700 to fix up Eric's backyard. Five
years ago, Eric put $12,500 into a home improvement account that has earned an average of
4.75% per year. Does Eric have enough money in his account to pay for the backyard fix-up?
A) Yes; Eric now has exactly $14,700 in his home improvement account.
B) Yes; Eric has $15,764.50 in his home improvement account.
C) No; Eric now has $10,519.32 in his home improvement account.
D) There is not enough information to answer this question.
15) Which of the following investments has a larger future value: A $100 investment earning
10% per year for 5 years or a $100 investment earning 5% per year for 10 years?
A) An investment of $100 invested at 10% per year for 5 years because it has a future value of
$161.05.
B) An investment of $100 invested at 10% per year for 5 years because it has a future value of
$162.89.
C) An investment of $100 invested at 5% per year for 10 years because it has a future value of
$161.05.
D) An investment of $100 invested at 5% per year for 10 years because it has a future value of
$162.89.
16) Which of the following investments has a larger future value: Investment A, a $1,000
investment earning 5% per year for 6 years, or Investment B, a $500 investment earning 10% per
year for 6 years, with a bonus of an extra $500 added at the end of the sixth year?
A) Investment B, with a future value of $1,386.
B) Investment A, with a future value of $1,386.
C) Investment A, with a future value of $1,340.
D) The investments have equal value.
17) You wish to make a substantial down payment on a lake cottage and you currently have
$15,725 invested at an annual rate of 2.50%. How much money will be in the account in 3.5
years if it continues to earn at its present rate?
A) $18,325
B) $20,579
C) $17,144
D) $19,605
18) If you invest $3,650 today, how much money will you have in 4 years?
A) $3,650
B) $4,437
C) This question cannot be answered because it is missing an annual rate of return.
D) This question cannot be answered because it is missing the type of investment made.
19) The current price on a 60-inch flat panel LCD HD television is $1,200. Big screen HD
television prices have dropped at an average rate of 12% per year in recent years. If you expect
this trend to continue, how much will this style of television cost in two years?
A) $1,122
B) $1,087
C) $1,008
D) $929
20) The financial aid office at your university has offered to pay your full annual tuition cost of
$19,000 this year, as long as you maintain a grade point average of 3.00. If tuition costs rise at a
rate of 8% per year while you are in college, but the financial aid office continues to pay exactly
$19,000 per year for your tuition, how much out-of-pocket tuition costs will you have your
senior year? NOTE: Think carefully about this problem when figuring the number of years from
the start of your freshman year to the start of your senior year, assuming normal progress toward
graduation in four years. Further, be aware that while tuition costs are rising your tuition is
covered up to only $19,000. You must pay any excess tuition costs.
A) $0
B) $4,202
C) $4,935
D) $5,130
21) Consider the TVM equation: An increase in the present value will decrease the future value,
other things remaining equal.
22) Consider a two-year investment: Given a constant and positive interest rate, the interest
earned in the second year will be greater than the interest earned in the first year (assuming
annual compounding).
23) Consider the TVM equation: A decrease in the interest rate will decrease the future value,
other things remaining equal.
24) Consider the TVM equation: A decrease in the time period will increase the future value,
other things remaining equal.
25) Consider the TVM equation: The future value is always greater than the present value, even
if the interest rate is negative.
27) $100 invested at a rate of 5% for 10 years has the same future value as $100 invested at 10%
compounded annually for 5 years.
28) $5,000 invested at an annual rate of 6% for 3 years has a smaller future value than $5,000
invested at an annual rate of 3% for 6 years.
29) If your bank offers a 5% annual rate of return compounded annually, then at the end of one
year your $1,000.00 deposit would grow by $50.00 to $1,050.00. However, in the second year,
your deposit would increase by $52.5025 to a total ending value of $1,102.50. Explain why the
second year earns more interest on the investment than the first year.
30) Sam wishes to invest $8,000 into an account earning 6% compounded annually. If he invests
the money today, how much will be in the account in 6 years? If he waits three years before
investing his $8,000 and invests that money for three years, will he earn one-half of the interest
earned in the first scenario since he had the same amount invested at the same rate but for only
one-half of the time? Explain how you arrived at your answer.
1) Which of the following actions will INCREASE the present value of an investment?
A) Decrease the interest rate.
B) Decrease the future value.
C) Increase the amount of time.
D) All of the above will increase the present value.
2) Which of the following actions will DECREASE the present value of an investment?
A) Decrease the interest rate.
B) Decrease the future value.
C) Decrease the amount of time.
D) All of the above will decrease the present value.
3) Which of the following formulas is CORRECT for finding the present value of an investment?
A) FV =
B) PV = FV × (1 + r)n
C) PV = FVn × (1 + r)
D) PV = FV ×
4) You have purchased a zero coupon bond that will pay $15,000 to your newborn child in 21
years. If this bond is discounted at a rate of 2.875% per year, what is today's price (present value)
for this bond?
A) $15,000
B) $9,348.25
C) $8,271.50
D) $5,654
5) A furniture store has a love seat on sale for $699.00, with the payment due one year from
today. The store is willing to discount the price at an annual rate of 5% if you pay today. What is
the amount if you pay today?
A) $665.71
B) $622.47
C) $608.21
D) $602.35
6) Your university is running a special offer on tuition. This year's tuition cost is $16,000. Next
year's tuition cost is scheduled to be $16,640. The university offers to discount next year's tuition
at a rate of 4% if you agree to pay both years' tuition in full today. How much is the total tuition
bill today if you take the offer?
A) $33118
B) $32,981
C) $32,080
D) $32,000
7) An investment promises a payoff of $995 two and one-half years from today. At a discount
rate of 4.5% per year, what is the present value of this investment?
A) $914.67
B) $891.32
C) $808.44
D) There is not enough information to answer this question.
8) Your family plans to spend $25,000 on a car for you upon graduation from college. If you will
graduate in three years and your family can earn 3.125% annually on their investment, how
much money must they set aside today for your car?
A) $23,243.66
B) $23,009.21
C) $22,795.45
D) $21,387.36
9) You intend to buy a vacation home in eight years and plan to have saved $75,000 for a down
payment. How much money would you have to place today into an investment that earns 9% per
year to have enough for your desired down payment?
A) $37,640
B) $37,218
C) $35,335
D) $34,989
10) In four years your oldest child will be in 10th grade, at which point you and your family plan
to vacation in Europe. You estimate that you will need $25,000 for the trip. How much do you
need to set aside today if you can place your money in an investment vehicle earning an average
of 4.25% per year?
A) $20,215.55
B) $20,998.34
C) $21,165.85
D) $21,435.77
11) Your grandparents leave on their dream vacation to Antarctica in three years. The cruise
vacation will cost them $24,000. If they have already saved $22,500 and are investing it at a rate
of 2.50% per year, will they have saved enough money for their trip?
A) No, because they forgot to factor in long underwear expenses.
B) No, to have enough money they would have already needed to save $23,375.
C) Yes, to have enough money they would have already needed to save $22,101.33 and they
already exceed that amount.
D) Yes, to have enough money they would have already needed to save $22,286.39 and they
already exceed that amount.
12) To determine the present value of a future amount, one should ________ the future cash
flows.
A) annuitize
B) compound
C) discount
D) multiply
13) The school district needs to pass a bond levy for funding to remodel existing schools and to
build new schools. Expenditures for the new and remodeled buildings will begin two years after
passage of the bond. If the school district receives all funding immediately after the passage of
the bond and can invest the funds at a rate of 2.75% per year, how large must the bond be for the
district to have $48,000,000 at the start of construction?
A) $48,000,000
B) $47,554,834
C) $46,556,397
D) $45,465,040
14) Your firm has sold a fleet of 50 cars to a local firm at a discounted price of $23,000 each (a
total of $1,150,000) due in six months. You are willing to discount the purchase price at an
annual rate of 3% if the firm pays cash today. What is the least amount of money you will accept
if the firm pays your company today?
A) $1,150,000
B) $1,133,129
C) $1,125,495
D) This problem cannot be answered because we have an annual interest rate but only one-half
year in time.
15) Your manufacturing firm has just secured a sale to the federal government with payment of
$480,000 due in nine months. You have asked your bank for cash today with the stipulation that
you will give the proceeds from the government contract to the bank in nine months. The bank
has agreed to your request if you allow them to discount the cash flows at an annual rate of 6%.
How much will the bank pay you today under this agreement?
A) $459,475
B) $466,889
C) $476,739
D) $480,000
16) Your trust fund will pay you $100,000 in six years when you turn 25. A shady financial
institution has encouraged you to sign away the rights to your trust fund in exchange for cash
today. Would you prefer that the financial institution use a discount rate of 8% or 10% to
determine the value of your lump sum payment? Why?
A) Use 8% because the lump sum payment of $62,741 is greater than the 10% discounted value
of $55,839.
B) Use 10% because the lump sum payment of $62,741 is greater than the 10% discounted value
of $55,839.
C) Use 8% because the lump sum payment of $63,017 is greater than the 10% discounted value
of $56,447.
D) Use 10% because the lump sum payment of $63,017 is greater than the 10% discounted value
of $56,447.
17) Your parts supplier gives you one-quarter of a year to pay for parts ordered today, or offers
you a discount if you pay cash at purchase. You have just purchased $94,500 worth of parts from
your supplier and the discount is at an annual rate of 10%. How much will you pay for the parts
if you pay today?
A) $94,500
B) $92,275
C) $94,144
D) $93,875
18) The Present Value Interest Factor (PVIF) is the reciprocal of the Future Value Interest Factor
(FVIF).
19) When solving for a present value, the interest rate is commonly referred to as the compound
rate, but when solving for the future value, the interest rate is called the discount rate.
