Chapter 04 – Time Value of Money 1: Analyzing Single Cash Flows
CHAPTER 4 – TIME VALUE OF MONEY 1: ANALYZING SINGLE CASH FLOWS
Questions
LG1 1. List and describe the purpose of each part of a time line with an initial cash inflow and a future
cash outflow. Which cash flows should be negative and which positive? Why?
LG2 2. How are the present value and future value related?
LG3 3. Would you prefer to have an investment earning 5 percent for 40 years or an investment
earning 10 percent for 20 years? Explain.
LG4 4. How are present values affected by changes in interest rates?
LG5 5. What do you think about the following statement? “I am going to receive $100 two years
from now and $200 three years from now, so I am getting a $300 future value.” How could the
two cash flows be compared or combined?
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Chapter 04 – Time Value of Money 1: Analyzing Single Cash Flows
LG6 6. Show how the Rule of 72 can be used to approximate the number of years to quadruple an
investment.
LG7 7. Without making any computations, indicate which of each pair has a higher interest rate?
a. $100 doubles to $200 in 5 years or 7 years.
b. $500 increases in 4 years to $750 or to $800.
c. $300 increases to $450 in 2 years or increases to $500 in 3 years.
LG8 8. A $1,000 investment has doubled to $2,000 in 8 years because of a 9 percent rate of return.
How much longer will it take for the investment to reach $4,000 if it continues to earn a 9
percent rate?
Problems
Basic Problems
LG1 4-1 Time Line Show the time line for a $500 cash inflow today, a $605 cash outflow in
year 2, and a 10 percent interest rate.
LG1 4-2 Time Line Show the time line for a $400 cash outflow today, a $518 cash inflow in year 3,
and a 9 percent interest rate.
The time line for this problem is:
Chapter 04 – Time Value of Money 1: Analyzing Single Cash Flows
LG2 4-3 One Year Future Value What is the future value of $500 deposited for one year earning a 8
percent interest rate annually.
LG2 4-4 One Year Future Value What is the future value of $400 deposited for one year earning an
interest rate of 9 percent per year?
LG3 4-5 Multiyear Future Value How much would be in your savings account in 11 years after
depositing $150 today if the bank pays 8 percent per year?
LG3 4-6 Multiyear Future Value Compute the value in 25 years of a $1,000 deposit earning 10
percent per year.
LG3 4-7 Compounding with Different Interest Rates A deposit of $350 earns the following interest
rates:
8 percent in the first year,
6 percent in the second year, and
5.5 percent in the third year.
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Education.
Chapter 04 – Time Value of Money 1: Analyzing Single Cash Flows
What would be the third year future value?
LG3 4-8 Compounding with Different Interest Rates A deposit of $750 earns interest rates of 9
percent in the first year and 12 percent in the second year. What would be the second year future
value?
LG4 4-9 Discounting One Year What is the present value of a $350 payment in one year when the
discount rate is 10 percent?
LG4 4-10 Discounting One Year What is the present value of a $200 payment in one year when the
discount rate is 7 percent?
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Chapter 04 – Time Value of Money 1: Analyzing Single Cash Flows
LG4 4-11 Present Value What is the present value of a $1,500 payment made in nine years when the
discount rate is 8 percent?
LG4 4-12 Present Value Compute the present value of an $850 payment made in 10 years when the
discount rate is 12 percent.
LG4 4-13 Present Value with Different Discount Rates Compute the present value of $1,000 paid in
three years using the following discount rates: 6 percent in the first year, 7 percent in the second
year, and 8 percent in the third year.
LG4 4-14 Present Value with Different Discount Rates Compute the present value of $5,000 paid in
two years using the following discount rates: 8 percent in the first year and 7 percent in the
second year.
LG6 4-15 Rule of 72 Approximately how many years does it take to double a $100 investment when
interest rates are 7 percent per year?
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Chapter 04 – Time Value of Money 1: Analyzing Single Cash Flows
LG6 4-16 Rule of 72 Approximately how many years does it take to double a $500 investment when
interest rates are 10 percent per year?
LG6 4-17 Rule of 72 Approximately what interest rate is needed to double an investment over five
years?
LG6 4-18 Rule of 72 Approximately what interest rate is earned when an investment doubles over 12
years?
LG7 4-19 Rates over One Year Determine the interest rate earned on a $1,400 deposit when $1,800
is paid back in one year.
LG7 4-20 Rates over One Year Determine the interest rate earned on a $2,300 deposit when $2,900
is paid back in one year.
intermediate problems
LG3 4-21 Interest-on-Interest Consider a $2,000 deposit earning 8 percent interest per year
for five years. What is the future value, and how much total interest is earned on the original
deposit vs. how much is interest earned on interest?
LG3 4-22 Interest-on-Interest Consider a $5,000 deposit earning 10 percent interest per year for 10
years. What is the future value, how much total interest is earned on the original deposit, and
how much is interest earned on interest?
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Chapter 04 – Time Value of Money 1: Analyzing Single Cash Flows
LG5 4-23 Comparing Cash Flows What would be more valuable, receiving $500 today or receiving
$625 in three years if interest rates are 7 percent? Why?
LG5 4-24 Comparing Cash Flows Which cash flow would you rather pay, $425 today or $500 in two
years if interest rates are 10 percent? Why?
LG5 4-25 Moving Cash Flows What is the value in year 3 of a $700 cash flow made in year 6 if
interest rates are 10 percent?
LG5 4-26 Moving Cash Flows What is the value in year 4 of a $1,000 cash flow made in year 6 if
interest rates are 8 percent?
PV = FVN / (1 + i)N
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Chapter 04 – Time Value of Money 1: Analyzing Single Cash Flows
LG5 4-27 Moving Cash Flows What is the value in year 10 of a $1,000 cash flow made in year 3 if
interest rates are 9 percent?
LG5 4-28 Moving Cash Flows What is the value in year 15 of a $250 cash flow made in year 3 if
interest rates are 11 percent?
LG7 4-29 Solving for Rates What annual rate of return is earned on a $1,000 investment when it
grows to $1,800 in six years?
LG7 4-30 Solving for Rates What annual rate of return is earned on a $5,000 investment when it
grows to $9,500 in five years?
LG8 4-31 Solving for Time How many years (and months) will it take $2 million to grow to $5
million with an annual interest rate of 7 percent?
Chapter 04 – Time Value of Money 1: Analyzing Single Cash Flows