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Chapter 09 - The Time Value of Money
9-1
1. An amount of money to be received in the future is worth less today than the stated
amount.
2. Discounting refers to the growth process that turns $1 today into a greater value several
periods in the future.
3. Compounding refers to the growth process that turns $1 today into a greater value several
periods in the future.
Chapter 09 - The Time Value of Money
5. The time value of money is not a useful concept in determining the value of a bond or in
capital investment decisions.
6. If a single amount were put on deposit at a given interest rate and allowed to grow, its
future value could be determined by reference to the future value of $1 table.
7. The time value of money concept is fundamental to the analysis of cash inflow and outflow
decisions covering periods of over one year.
8. The future value is the same concept as the way money grows in a bank account.
Chapter 09 - The Time Value of Money
9-3
9. Cash flow decisions that ignore the time value of money will probably not be as accurate as
those decisions that do rely on the time value of money.
10. The present value of a positive future inflow can become negative as discount rates
become higher and higher.
11. The interest factor for a future value (FVIF) is equal to (1 + i)n.
12. The formula PV = FV(1 + n)i will determine the present value of $1.
Chapter 09 - The Time Value of Money
9-4
13. In determining the interest factor (IF) for the present value of $1, one could use the
reciprocal of the IF for the future value of $1 at the same rate and time period.
14. To determine the current worth of 4 annual payments of $1,000 at 4%, one would refer to
a table for the present value of $1.
15. As the interest rate increases, the interest factor (IF) for the present value of $1 increases.
16. The interest factor for the present value of a single amount is the inverse of the future
value interest factor.
17. The interest factor for the present value of a single sum is equal to (1 + i)/i.
Chapter 09 - The Time Value of Money
18. Higher interest rates (discount rates) reduce the present value of amounts to be received in
the future.
19. In determining the future value of an annuity, the final payment is not compounded at all.
20. The future value of an annuity assumes that the payments are received at the end of the
year and that the last payment does not compound.
21. The future value of an annuity table provides a short-cut for calculating the future value of
a steady stream of payments, denoted as A. The same value can be calculated directly from
the following equation:
Chapter 09 - The Time Value of Money
22. The present value of an annuity table provides a short-cut for calculating the future value
of a steady stream of payments, denoted as A. The same value can be calculated directly from
the following equation:
23. The amount of annual payments necessary to accumulate a desired total can be found by
reference to the present value of an annuity table.
24. If an individual's cost of capital were 6%, he/she would prefer to receive $110 at the end
of one year rather than $100 right now.
Chapter 09 - The Time Value of Money
25. In evaluating capital investment projects, current outlays must be judged against the
current value of future benefits.
26. The farther into the future any given amount is received, the larger its present value.
27. The interest factor for the future value of an annuity is simply the sum of the interest
factors for the future value using the same number of periods.
28. An annuity is a series of consecutive payments of equal amount.
Chapter 09 - The Time Value of Money
29. Using semi-annual compounding rather than annual compounding will increase the future
value of an annuity.
30. When the inflation rate is zero, the present value of $1 is identical to the future value of
$1.
31. Pension fund retirement accounts use the present value of an annuity to calculate the
ending value upon retirement.
32. The amount of annual payments necessary to repay a mortgage loan can be found by
reference to the present value of an annuity table.
Chapter 09 - The Time Value of Money
33. In paying off a mortgage loan, the amount of the periodic payment that goes toward the
reduction of principal increases over the life of the mortgage.
34. The time value of money concept becomes less critical as the prime rate increases.
35. Discounted at 6%, $1000 received three years from now is worth less than $800 received
today.
Chapter 09 - The Time Value of Money
36. Discounted at 10%, $1000 received at the end of each year for three years is worth less
than $2,700 received today.
37. When adjusting for semi-annual compounding of an annuity, the adjustments include
multiplying the periods and annuity by 2.
38. Calculation of the yield of an investment provides the total return over multiple years.
39. Under what conditions must a distinction be made between money to be received today
and money to be received in the future?
Chapter 09 - The Time Value of Money
40. As the compounding rate becomes lower and lower, the future value of inflows
approaches
41. If you invest $10,000 at 10% interest, how much will you have in 10 years?
Chapter 09 - The Time Value of Money
42. In determining the future value of a single amount, one measures
43. The concept of time value of money is important to financial decision making because
44. As the discount rate becomes higher and higher, the present value of inflows approaches
Chapter 09 - The Time Value of Money
45. How much must you invest at 8% interest in order to see your investment grow to $8,000
in 10 years?
46. An annuity may be defined as
47. You are to receive $12,000 at the end of 5 years. The available yield on investments is
6%. Which table would you use to determine the value of that sum today?
Chapter 09 - The Time Value of Money
48. As the interest rate increases, the present value of an amount to be received at the end of a
fixed period
49. As the time period until receipt increases, the present value of an amount at a fixed
interest rate
50. To find the yield on investments which require the payment of a single amount initially,
and which then return a single amount some time in the future, the correct table to use is
Chapter 09 - The Time Value of Money
51. Ali Shah sets aside 2,000 each year for 5 years. He then withdraws the funds on an equal
annual basis for the next 4 years. If Ali wishes to determine the amount of the annuity to be
withdrawn each year, he should use the following two tables in this order:
52. To save for her newborn son's college education, Lea Wilson will invest $1,000 at the
beginning of each year for the next 18 years. The interest rate is 12 percent. What is the future
value?
Chapter 09 - The Time Value of Money
53. If you were to put $1,000 in the bank at 6% interest each year for the next ten years, which
table would you use to find the ending balance in your account?
54. The IF for the future value of an annuity is 4.641 at 10% for 4 years. If we wish to
accumulate $8,000 by the end of 4 years, how much should the annual payments be?
Chapter 09 - The Time Value of Money
55. Mr. Blochirt is creating a college investment fund for his daughter. He will put in $1,000
per year for the next 15 years and expects to earn a 6% annual rate of return. How much
money will his daughter have when she starts college?
56. Mr. Nailor invests $5,000 in a money market account at his local bank. He receives annual
interest of 8% for 7 years. How much return will his investment earn during this time period?
Chapter 09 - The Time Value of Money
57. Lou Lewis borrows $10,000 to be repaid over 10 years at 9 percent. Repayment of
principal in the first year is:
58. Sharon Smith will receive $1 million in 50 years. The discount rate is 13%. As an
alternative, she can receive $1,000 today. Which should she choose?
Chapter 09 - The Time Value of Money
59. Pedro Gonzalez will invest $5,000 at the beginning of each year for the next 9 years. The
interest rate is 8 percent. What is the future value?
60. Ambrin Corp. expects to receive $2,000 per year for 10 years and $3,500 per year for the
next 10 years. What is the present value of this 20 year cash flow? Use an 11% discount rate.
Chapter 09 - The Time Value of Money
61. Dr. J. wants to buy a Dell computer which will cost $3,000 three years from today. He
would like to set aside an equal amount at the end of each year in order to accumulate the
amount needed. He can earn 8% annual return. How much should he set aside?
62. Mr. Fish wants to build a house in 8 years. He estimates that the total cost will be
$150,000. If he can put aside $10,000 at the end of each year, what rate of return must he earn
in order to have the amount needed?
