8) Kirby Puckett became the first $3,000,000 man in major league baseball in 1990. By 2008, A-
Rod was bringing in $27,500,000 per year. Did the annual change in the highest annual baseball
salary rise more rapidly over this time period than from 1930 to 1990? Babe Ruth had the highest
salary and made $80,000 in 1930.
A) Yes, because the annual rate of change was 29.17% in the more recent period and only
36.67% in the earlier period.
B) No, because the annual rate of change was 29.17% in the more recent period and 36.67% in
the earlier period.
C) Yes, because the annual rate of change was 13.10% in the more recent period and only 6.23%
in the earlier period.
D) There is not enough information provided to answer this question.
9) In January of 1997, the U.S. Consumer Price Index (CPI) stood at 159.1. By January of 2017,
the level had risen to 242.84. What was the average annual rate of inflation over this time period
as measured by the CPI?
A) 2.14%
B) 3.35%
C) 2.35%
D) 2.60%
10) The survey results from the National Association of Colleges and Employers (NACE) show
the average annual increases in salaries for new accounting graduates to be 3.42% since the year
2000. If new starting salaries in accounting were $36,919 in 2000, what were they in 2016?
A) $45,757
B) $53,444
C) $63,230
D) $68,518
11) Your finance professor suggests that you should have $3,000,000 in your retirement portfolio
before you even THINK about retiring. Recently, your aunt sold valuable California real estate
and handed you a check for $387,500. (This is the amount you have after paying taxes. She is
now your favorite aunt.) How much of the $387,500 must you set aside today if you invest a
portion of the money at an annual rate of 7.5% and you wish to retire in 38 years with the
amount suggested by your finance professor?
A) $169,086
B) $192,132
C) $306,187
D) At an annual rate of return of 7.5.0%, $387,500 is not a large enough investment to reach the
goal amount of $3,000,000 in 38 years.
12) You plan to place a $55,000 down payment on a lake cabin in Southern Oregon in five years.
If you invest in a long-term CD earning an annual rate of 4.50%, how much would you need to
invest today to have enough for the down payment in five years?
A) $23,326
B) $30,605
C) $44,135
D) $46,264
13) Rick decided he was tired of being a poor college student when he visited a local electronics
store and experienced its finest home theatre system. He determined that he would invest today a
portion of the remaining money he earned last summer cleaning animal cages at the veterinary
clinic. He plans to invest the money into an international mutual fund for 2.5 years and expects
to earn an average annual rate of return of 15%. If Rick wants to have $5,000 in the account at
the end of this time, how much must he invest today?
A) $2,253
B) $3,048
C) $3,526
D) $3,891
14) You need $18,000 at the end of 4 years. If you can earn 0.325% per month, how much would
you need to invest today to meet your objective?
A) $11,600
B) $13,319
C) $14,391
D) $15,404
15) Your friend, Justin, started college at the age of 18 with $40,559 already saved. He has this
money because 18 years ago when he was born his parents placed money into a special college
savings account earning 7.00% per year. How much money did Justin’s parents place into his
college account?
A) $12,000
B) $18,000
C) $19,262
D) $21,000
16) You know that regular tax-deferred investments are a popular investment choice for many
people preparing for retirement. Did you know that if you invest $2,000 today and at the end of
every year for 40 years at an annual rate of 10% that you will have grown your portfolio to a
value of $975,704 at the end of that time? How much of that future value dollar amount comes
from the $2,000 investment you made today?
A) $975,704
B) $885,185
C) $23,798
D) $90,519
17) If you invest $5,000 today at an annual interest rate of 5.35%, how much money will you
have for your daughter’s college education in 18 years?
A) $5,603
B) $10,000
C) $12,776
D) There is not enough information to answer this question.
18) You won the state lottery and took the payout as a $1,823,475 lump sum today. Your spouse
has decided that you need to invest this money for the next 9 years and can expect it to earn an
average annual rate of return of 8.00%. If this comes to pass, how much money will be in the
account at the end of the period?
A) $8,471,253
B) $3,645,135
C) $2,567,586
D) $1,890,471
19) If you can earn 5.25% per year on your investments, how long will it take to double your
money?
A) 6.31 years
B) 19.05 years
C) 13.55 years
D) There is not enough information to answer this question.
20) Your father spent all of his adult life working in a small T-shirt making firm. His first year
sales were $98,000 and his last year sales were $350,000. If the firm grew at an average rate of
3.35% per year, how many years did your father sell T-shirts at his firm?
A) 43.16 years
B) 40.00 years
C) 38.63 years
D) 25.91 years
21) Your production manager informs you that currently the firm is producing 1,348 heating
units per month but has plans to increase production at a rate of 5% per month until the firm is
producing 3,000 units per month. How many months will this take?
A) 16.40 months
B) 15.07 months
C) 14 months
D) There is not enough information to answer this question.
22) Antonio made $18,000 in the first movie he ever starred in. He soon made more and more
movies and more and more money. At a 46.18% rate of salary increase per movie, how many
movies did he make in order to earn $5,350,000 in a single movie?
A) 84 movies
B) 34 movies
C) 22 movies
D) 15 movies
23) Given a time period, an interest rate, and a future value, a person could solve for a present
value.
24) You have $5,000 in an index mutual fund. At an average annual rate of return of 10% per
year, this investment should exceed a value of $500,000 by the time you retire in 40 years.
25) You win the $5,000,000 lottery that pays you $250,000 per year over a 20-year period. Given
negative interest rates, the lottery has a present value that is less than $5,000,000.
26) If interest rates are positive, then discounting increases the future value of an investment
while compounding reduces the present value of an investment.
27) A plant nursery pays $2,000 for 800 one-gallon flowering trees, plants them, and forgets
them. Five years later, the nursery is able to sell each of the 100 trees that survived for $50 each.
What is the rate of return on its total investment?
28) If college tuition and fees increase at an annual rate of 7% per year, and your little sister is
currently starting her freshman year in high school, what is the expected cost of her first year of
college in four years if tuition and fees are currently $6,850 per year? How much for the start of
her senior year of college starting three years after that?
45
Copyright © 2019 Pearson Education, Inc.
3.5 Doubling of Money: The Rule of 72
1) Lance has $3,500 but needs $7,000 to purchase a new golf cart. If he can invest his money at a
rate of 12% per year, approximately how many years will it take the money in Lance’s account to
grow to $7,000? Use the Rule of 72 to determine your answer.
Note: The bicycle’s price may have changed by the time Lance’s account reaches a value of
$7,000.
A) 2 years
B) 4 years
C) 6 years
D) 8 years
2) You can invest your money at a rate of 7% per year. At this rate it will take you just over
________ years to double your money. Use the Rule of 72 to determine your answer.
A) 4
B) 10
C) 5.5
D) There is not enough information to answer this question.
3) What annual rate of return must you earn to double your money in about 9 years? Use the
Rule of 72 to determine your answer.
A) You would need to earn an annual rate of return of about 12%.
B) You would need to earn an annual rate of return of about 10%.
C) You would need to earn an annual rate of return of about 8%.
D) There is not enough information to answer this question.
4) The dividends per share paid by Artisan Industries Inc. (AI) doubled from a starting value of
$1.50 in 2010 to a value of $3.00 in 2016 (a six-year period). What was the approximate average
annual rate of growth of AI’s dividends per share? Use the Rule of 72 to determine your answer.
A) FFF’s dividends grew at an annual rate of approximately 12% per year.
B) FFF’s dividends grew at an annual rate of approximately 10% per year.
C) FFF’s dividends grew at an annual rate of approximately 8% per year.
D) FFF’s dividends grew at an annual rate of approximately 6% per year.
5) In your first year out of college you hope to earn $30,000 per year. How many years will you
have to work until you earn $120,000 if your income increases at a rate of 10% per year? Use the
Rule of 72 to determine your answer.
A) You would need to work for just over 14 years to reach an income level of $100,000 per year.
B) You would need to work for just over 10 years to reach an income level of $100,000 per year.
C) You would need to work for just over 7 years to reach an income level of $100,000 per year.
D) You would need to work for just over 5 years to reach an income level of $100,000 per year.
6) A manufacturer of Virtual Reality headsets has seen sales increase from 25,000 units per year
to 100,000 units per year in 8 years. What has been the firm’s average annual rate of increase in
the number of television sets sold? Use the Rule of 72 to determine your answer.
A) The average annual rate of change has been between 10% and 11%.
B) The average annual rate of change has been between 18% and 19%.
C) The average annual rate of change has been between 15% and 16%.
D) There is not enough information to answer this question.
7) The Rule of 72 is a rule of thumb for estimating the length of time necessary to double your
money, given an interest rate.
8) The Rule of 72 is a rule of thumb for estimating the interest rate necessary to double your
money, given a period of time.
9) The Rule of 72 can be used to quickly estimate interest rates necessary to double your money
in a given time period without the use of a spreadsheet or calculator. However, the rule does
NOT work for estimating growth rates.
10) Given enough time, you could double your money with a risk-free investment.
11) Assume you put $2,000 into a tax-free investment and leave it there for 45 years at an annual
rate of 8%. According to the Rule of 72, your investment will grow to a value of about $64,000.
12) The television commercial pitchman tells you he can double your money with a risk-free
investment in just 10 years. If this is true, what interest rate must this risk-free investment earn
on an annual basis? Solve this question using the Rule of 72 and then in a more exact fashion
using a formula, your calculator, or computer. In today’s rate environment, is the interest rate that
you solved for a realistic annual rate of return for a risk-free investment?
13) What is the Rule of 72? Why do you think the Rule of 72 came into widespread use? Give an
example of where you think the rule could be useful.