20) Given an interest rate of 0%, the present value of $1,500 to be received 5 years in the future
is less than $1,500.
21) Consider the TVM equation: Present values and interest rates are inversely related.
22) Consider the TVM equation: The greater the interest rate, other things remaining equal, the
greater the present value.
23) Amy has always planned to save enough money to pay cash for her first new car. If Amy
increases the rate she earns on her savings, then she will have to save more money today to buy
her car at the same date in the future.
24) $1,000 received 5 years from today discounted at an annual rate of 10% has a smaller present
value than $1,000 received 10 years from today discounted at an annual rate of 5%.
25) Consider the TVM equation: Present value and time period are inversely related.
26) Write the equation for present value. How are prices and interest rates related? Refer to your
equation when answering the first part of this question. Give an example of a real-world situation
in which knowing the relationship between prices and interest rates would be valuable.
27) Harold’s parents have offered him a $10,000 high school graduation gift with an option for
another $20,000 upon graduation from college in four years. His friends tell him this is a $30,000
gift from his parents, but Harold already knows something about the time value of money. If the
expected inflation rate over the next four years is expected to be 4% per year, what does Harold
think the gift is worth in today’s dollars? How should he explain his thinking to his friends?
28) Compare and contrast the discount rate with the compound (or growth) rate.
1) In the equation r = (FV/PV)1/n – 1, the r is sometimes referred to as the ________.
A) interest rate
B) discount rate
C) growth rate
D) All of the above
2) The question “How much will I have in my account at a specific point in the future, given a
specific interest rate?” is best answered by which form of the TVM equation?
A) FV =
B) FV = PV × (1 + r)n
C) FV = (FV/PV)1/n -1
D)
FV =
3) The question “What is the current value of an amount of cash that will be received at a
specific time in the future?” is best answered by which form of the TVM equation?
A) PV =
B) PV = PV × (1 + r)n
C) PV = (FV/PV)1/n – 1
D) PV =
4) The question “At what rate is my money growing over time?” is best answered by which form
of the TVM equation?
A) r =
B) r = PV × (1 + r)n
C) r = (FV/PV)1/n – 1
D) r =
5) The question “How long will I have to wait to reach a certain future value?” is best answered
by which form of the TVM equation?
A) n =
B) n = PV × (1 + r)n
C) n = (FV/PV)1/n – 1
D) n =
6) Dividend growth rate is important to many investors. You are considering investing in a firm
after looking at the firm’s dividends over a six-year period. At the end of the year 2010, the firm
paid a dividend of $0.98. At year-end 2016, it paid a dividend of $1.64. What was the average
annual growth rate of dividends for this firm?
A) 8.25%
B) 9.86%
C) 8.96%
D) There is not enough information to answer this question.
7) Five years ago, Maria’s annual salary was $73,500. Today, she earns $91,900. What has been
the average annual percentage rate of growth of Maria’s salary?
A) $3,680 per year
B) 8.89%
C) 6.27%
D) 4.57%
8) You gave your little sister two rabbits for Easter three years ago and now she has 64 of the
cute little bunnies. What is the average annual rate of increase in the number of rabbits your
sister owns? Note: Your parents are not very pleased with you right now.
A) 217.5%
B) 400.0%
C) 521.8.00%
D) The TVM equations are designed for currency amounts and cannot be used for non-financial
calculations such as this one.
9) Family Construction had sales three years ago of $2,150,000. This year their sales hit
$2,900,000. What has been the firm’s average annual rate of growth of sales?
A) 30.56%
B) 10.49%
C) $350,000 per year
D) None of the above
10) The Johnstown School District had 3,171 students enrolled four years ago. Today, the district
enrollment is 2,618 students. What has been the annual rate of change of student enrollment in
the School District over this time period?
A) -5.44%
B) -4.35%
C) -4.68%
D) 4.35%
11) You currently have $3,500 invested at an annual rate of 8%. How long will it take for this
investment to grow to a value of $5,000?
A) 4.63 years
B) 5.00 years
C) 5.60 years
D) 4.37 years
12) You have saved $1,250 for a used motorcycle that has a current price of $1,550. If your
money is sitting in an account earning 2.25% per year, how long will it take for this account to
grow to $1,550? Note: The motorcycle’s price may have changed by the time your account
reaches a value of $1,550.
A) 9.04 months
B) 9.67 years
C) 9.04 years
D) 9.67 months
13) Drew is taking over as Chief Marketing Officer at SouthWest Foods. She has pledged to
increase sales from their current level of $8,000,000 at a rate of 11% per year until the firm hits
sales of $15,000,000 per year. How long will it take the firm to hit the target goal at this rate of
increase?
A) 5.18 years
B) 5.36 years
C) 6.02 years
D) At that rate, Madison will never reach the target sales level in her lifetime.
14) Upon taking his first job out of college, your Dad earned an annual salary of $33,000 and set
a goal to earn $100,000 per year. If his salary increased at an average annual rate of 5.5%, how
long did it take to reach his goal?
A) At that rate of growth, your Dad still has not earned $100,000 in a single year.
B) 8.54 years
C) 16.31 years
D) 20.71 years
15) Your grandfather likes to tell the story about how he started his ranch with 100 head of cattle
and grew the ranch to 2,500 head of cattle. He said “My plan was simple: grow the number of
head of cattle at a rate of 10% per year.” Your grandfather reached his goal before he retired.
How long did it take him?
A) 38.63 years
B) 33.77 years
C) 31.43 years
D) 27.65 years
16) Consider the TVM equation: the variable “r” may be defined as the discount rate or the
growth rate depending upon how the equation is being used.
17) Even if you are given a present value, a future value, and an interest rate, solving for the time
period “n” is still a trial-and-error process.
18) Even if you are given a present value, a single future value, and a time period, solving for the
rate of return, r, is still a trial-and-error process.
19) Other things remaining equal, the price today and the growth rate are inversely related.
20) You have just won the university lottery. If you graduate, you will receive a refund equal to
the amount of tuition you paid in your first four years of school. However, you need money now
and a firm that specializes in buying expected future cash flows has offered to discount the
lottery winnings at a rate of 8% and pay you cash today in exchange for your future lottery
winnings. Since you have studied finance, you insist that they discount the cash flows at 12%
instead of 8% because there is some risk as to the certainty of your graduating. If the firm agrees
to your demand, then this means they will increase the present value of what they will pay you
today.
21) Current annual dividends for Simpsons Frozen Foods Inc., are $1.35 per share. Four years
ago, dividends per share were exactly $1.00. What has been the rate of growth for Simpsons’
dividends per share?
22) At your birth, your grandparents put $5,000 into a college fund for you. Now you want to use
the fund to pay your first year of college costs of $23,000. To have enough money in your
college fund for your stated purpose, what annual rate of return would have to have been earned
on the account over an 18-year period?
23) You made your first $3,000 deposit today into a retirement account earning an average
annual rate of 6%. How long will it take your deposit to reach a value of $50,000? How long will
it take if instead you invest the money into an account earning 10% per year? After making your
calculations, how does this information affect your decision-making regarding long-term
investments?
1) In 1930, the highest paid player in major league baseball was Babe Ruth of the New York
Yankees, with an annual salary of $80,000. In 2017, the highest paid player in major league
baseball was Clayton Kershaw of the Los Angeles Dodgers with a salary of $35,571,000. What
was the average annual rate of growth in the top baseball salary over this time period?
A) 7.26%
B) 7.96%
C) 9.23%
D) 10.41%
2) In 1970, before the era of major league baseball free agency, the minimum player salary was
$12,000. In 1975, the minimum salary was $16,000. What was the average annual growth in the
minimum salary in major league baseball over those five years?
A) 13.40%
B) 2.67%
C) 5.92%
D) 15.00%
3) In 1975, the era of major league baseball free agency began. The average player salary was
$16,000. In 1980, the average salary was $30,000. What was the average annual growth in the
minimum salary in major league baseball over those five years?
A) 37.50%
B) 13.40%
C) 5.92%
D) 10.67%
4) Median U.S. wages in 2014 were $53,675, compared to the median wage in 1990 of $28,960.
What was the average annual increase in median wages over this 24-year period?
A) 1.31%
B) 2.60%
C) 4.50%
D) 4.58%
5) Gasoline cost $.10 per gallon in 1930. Over the next 70 years, the price rose at an average rate
of 4.00% per year. Based on this information, what was the average price of a gallon of gas in
1990?
A) $1.34 per gallon
B) $1.56 per gallon
C) $2.28 per gallon
D) $2.37 per gallon
6) For much of the 20th century, new car prices rose at an average annual rate of 5.89%. Given a
beginning new car price of $900, how long did it take for the average new car price to rise to
$27,865? Please round to the nearest year.
A) 40 years
B) 60 years
C) 70 years
D) 100 years
7) Buying your own home is often mentioned as “the best investment you can make.” In 1964,
the average home sale price was $19,600. By 2009, the average home sale price had risen to
$272,900. What was the average annual rate of change in the price of houses over this 45 year
time period?
A) 3.74% per year
B) 6.03% per year
C) 10.52% per year
D) 12.16% per year