Deck 9: The Time Value of Money

Question 1

An amount of money to be received in the future is worth less today than the stated amount.

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

The future value is the same concept as the way money grows in a bank account.

Answer 3

True

Question 4

The interest factor for the present value of a single sum is equal to (1 + i)/i.

Question 5

As the interest rate increases, the interest factor (IF) for the present value of $1 increases.

Question 6

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.

Question 7

The time value of money concept is fundamental to the analysis of cash inflow and outflow decisions covering periods of over one year.

Question 8

The interest factor for the future value of a single sum is equal to (1 + n)ⁱ.

Question 9

The interest factor for a future value (FV_IF) is equal to (1 + i)ⁿ.

Question 10

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.

Question 11

The interest factor for the present value of a single amount is the inverse of the future value interest factor.

Question 12

In determining the future value of an annuity, the final payment is not compounded at all.

Question 13

The time value of money is not a useful concept in determining the value of a bond or in capital investment decisions.

Question 14

Compounding refers to the growth process that turns $1 today into a greater value several periods in the future.

Question 15

Discounting refers to the growth process that turns $1 today into a greater value several periods in the future.

Question 16

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.

Question 17

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.

Question 18

Higher interest rates (discount rates) reduce the present value of amounts to be received in the future.

Question 19

The present value of a positive future inflow can become negative as discount rates become higher and higher.

Question 20

The formula PV = FV(1 + n)ⁱ will determine the present value of $1.

Question 21

Calculation of the yield of an investment provides the total return over multiple years.

Question 22

Using semi-annual compounding rather than annual compounding will increase the future value of an annuity.

Question 23

The time value of money concept becomes less critical as the prime rate increases.

Question 24

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.

Question 25

The farther into the future any given amount is received, the larger its present value.

Question 26

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:

Question 27

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.

Question 28

Under what conditions must a distinction be made between money to be received today and money to be received in the future?

A) A period of recession.
B) When idle money can earn a positive return.
C) When there is no risk of nonpayment in the future.
D) When current interest rates are different from expected future rates.

Question 29

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.
(App. B: 6%, 1 period)
= $110 x .0.943 = $104

Question 30

When adjusting for semi-annual compounding of an annuity, the adjustments include multiplying the periods and annuity by 2.

Question 31

In evaluating capital investment projects, current outlays must be judged against the current value of future benefits.

Question 32

As the compounding rate becomes lower and lower, the future value of inflows approaches

A) 0
B) the present value of the inflows
C) infinity
D) need more information

Question 33

When the inflation rate is zero, the present value of $1 is identical to the future value of $1.

Question 34

The amount of annual payments necessary to accumulate a desired total can be found by reference to the present value of an annuity table.

Question 35

Discounted at 6%, $1000 received three years from now is worth less than $800 received today.
(App. B: 3 periods, 6%)
= $1,000 x .840 = $840

Question 36

The amount of annual payments necessary to repay a mortgage loan can be found by reference to the present value of an annuity table.

Question 37

Discounted at 10%, $1000 received at the end of each year for three years is worth less than $2,700 received today.
PV_A = A $\times$ PV_IFA (App. D: 3 periods, 10%)
= $1,000 $\times$ .2.487 = $2,487

Question 38

An annuity is a series of consecutive payments of equal amount.

Question 39

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:

Question 40

Pension fund retirement accounts use the present value of an annuity to calculate the ending value upon retirement.

Question 41

As the discount rate becomes higher and higher, the present value of inflows approaches

A) 0
B) minus infinity
C) plus infinity
D) need more information

Question 42

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

A) the present value of $1
B) the future value of $1
C) present value of an annuity of $1
D) (a) and (b) above.

Question 43

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?

A) $7,690.
B) $34,931.
C) $63,440.
D) $62,440.

Question 44

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?

A) Present value of $1
B) Future value of $1
C) Present value of an annuity of $1
D) Future value of an annuity of $1

Question 45

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.

A) $19,034
B) $27,870
C) $32,389
D) none of these

Question 46

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?

A) $11,250
B) $12,263
C) $24,003
D) $23,276

Question 47

As the time period until receipt increases, the present value of an amount at a fixed interest rate

A) decreases.
B) remains the same.
C) increases.
D) Not enough information to tell.

Question 48

Sharon Smith will receive $1 million in 50 years. The discount rate is 14%. As an alternative, she can receive $1,000 today. Which should she choose?

A) the $1 million dollars in 50 years.
B) $2,000 today.
C) she should be indifferent.
D) need more information.

Question 49

An annuity may be defined as

A) a payment at a fixed interest rate.
B) a series of payments of unequal amount.
C) a series of yearly payments.
D) a series of consecutive payments of equal amounts.

Question 50

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?

A) $58,471.
B) $62,440.
C) $67,435.
D) $72,435.

Question 51

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?

A) $2,915
B) $3,570
C) $6,254
D) $8,570

Question 52

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?

A) Present value of an annuity of $1
B) Future value of an annuity
C) Present value of $1
D) Future value of $1

Question 53

The concept of time value of money is important to financial decision making because

A) it emphasizes earning a return on invested capital.
B) it recognizes that earning a return makes $1 worth more today than $1 received in the future.
C) it can be applied to future cash flows in order to compare different streams of income.
D) all of these

Question 54

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:

A) present value of an annuity of $1; future value of an annuity of $1
B) future value of an annuity of $1; present value of an annuity of $1
C) future value of an annuity of $1; present value of a $1
D) future value of an annuity of $1; future value of a $1

Question 55

If you invest $10,000 at 10% interest, how much will you have in 10 years?

A) $13,860
B) $25,940
C) $3,860
D) $80,712

Question 56

As the interest rate increases, the present value of an amount to be received at the end of a fixed period

A) increases.
B) decreases.
C) remains the same.
D) Not enough information to tell.

Question 57

In determining the future value of a single amount, one measures

A) the future value of periodic payments at a given interest rate.
B) the present value of an amount discounted at a given interest rate.
C) the future value of an amount allowed to grow at a given interest rate.
D) the present value of periodic payments at a given interest rate.

Question 58

Lou Lewis borrows $10,000 to be repaid over 10 years at 9 percent. Repayment of principal in the first year is:

A) $1,558
B) $658
C) $742
D) $885

Question 59

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?

A) $2,500
B) $2,000
C) $1,724
D) none of these

Question 60

How much must you invest at 8% interest in order to see your investment grow to $8,000 in 10 years?

A) $3,070
B) $3,704
C) $3,105
D) none of these

Question 61

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?

A) Between 17% and 18%
B) Between 15% and 16%
C) 12%
D) None of these

Question 62

Mr. Darden is selling his house for $200,000. He bought it for $164,000 ten years ago. What is the annual return on his investment?

A) 2%
B) Between 3% and 5%
C) 10%
D) None of these

Question 63

A home buyer signed a 20-year, 8% mortgage for $72,500. Given the following information, how much should the annual loan payments be?
Present value of $1 PV_IF= .215
Future value of $1 FV_IF= 4.661
Present value of annuity PV_IFA= 9.818
Future value of annuity FV_IFA= 45.762

A) $1,584
B) $7,384
C) $15,555
D) $15,588

Question 64

Increasing the number of periods will increase all of the following except

A) the present value of an annuity.
B) the present value of $1.
C) the future value of $1.
D) the future value of an annuity.

Question 65

Mike Carlson will receive $12,000 a year from the end of the third year to the end of the 12thyear (10 payments). The discount rate is 10%. The present value today of this deferred annuity is:

A) $61, 450
B) $42,185
C) $55,379
D) $60,909

Question 66

Mr. Smith has just invested $10,000 for his son (age 7). The money will be used for his son's education 15 years from now. He calculates that he will need $100,000 for his son's education by the time the boy goes to school. What rate of return will Dr. Stein need to achieve this goal?

A) between 9% and 10%
B) between 16% and 17%
C) between 10% and 11%
D) between 15% and 16%

Question 67

You will deposit $2,000 today. It will grow for 6 years at 10% interest compounded semiannually. You will then withdraw the funds annually over the next 4 years. The annual interest rate is 8%. Your annual withdrawal will be:

A) $2,340
B) $4,332
C) $797
D) $1,085

Question 68

The shorter the length of time between a present value and its corresponding future value,

A) the lower the present value, relative to the future value.
B) the higher the present value, relative to the future value.
C) the higher the interest rate used in the present-valuation.
D) none of these.

Question 69

John Doeber borrowed $150,000 to buy a house. His loan cost was 6% and he promised to repay the loan in 15 equal annual payments. What is the principal outstanding after the first loan payment?

A) $143,555
B) $134,560
C) $141,200
D) None of these

Question 70

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?

A) $879
B) $627
C) $924
D) $1,243

Question 71

Football player Walter Johnson signs a contract calling for payments of $250,000 per year, to begin 10 years from now. To find the present value of this contract, which table or tables should you use?

A) The future value of $1
B) The future value of an annuity of $1 and the future value of $1
C) The present value of an annuity of $1 and the present value of $1
D) None of these

Question 72

The future value of a $500 investment today at 10 percent annual interest compounded semiannually for 5 years is

A) $805
B) $814
C) $750
D) $923

Question 73

A dollar today is worth more than a dollar to be received in the future because

A) risk of nonpayment in the future.
B) the dollar can be invested today and earn interest.
C) inflation will reduce purchasing power of a future dollar.
D) None of these.

Question 74

The higher the rate used in determining the future value of a $1 annuity,

A) the smaller the future value at the end of the period.
B) the greater the future value at the end of a period.
C) the greater the present value at the beginning of a period.
D) none of these - the interest has no effect on the future value of an annuity.

Question 75

John Doeber borrowed $150,000 to buy a house. His loan cost was 6% and he promised to repay the loan in 15 equal annual payments. How much are the annual payments?

A) $3,633
B) $9,250
C) $13,113
D) $15,445

Question 76

A retirement plan guarantees to pay to you or your estate a fixed amount for 20 years. At the time of retirement you will have $73,425 to your credit in the plan. The plan anticipates earning 9% interest. Given the following information, how much will your annual benefits be?
Present value of $1 PV_IF= .178
Future value of $1 FV_IF= 5.604
Present value of annuity PV_IFA= 9.129
Future value of annuity FV_IFA= 51.16

A) $1,435
B) $13,070
C) $8,043
D) $13,102

Question 77

Joe Nautilus has $210,000 and wants to retire. What return must his money earn so he may receive annual benefits of $30,000 for the next 10 years.

A) 12%
B) Between 12% and 13%
C) About 7%
D) Greater than 15%

Question 78

After 10 years, 100 shares of stock originally purchased for $500 was sold for $900. What was the yield on the investment? Choose the closest answer.

A) 19%
B) 2.5%
C) 8.5%
D) 6%

Question 79

Carol Thomas will pay out $6,000 at the end of the year 2, $8,000 at the end of year 3, and receive $10,000 at the end of year 4. With an interest rate of 13 percent, what is the net value of the payments vs. receipts in today's dollars?

A) $7,326.
B) $10,242.
C) $16,372.
D) $4,112.

Question 80

Babe Ruth Jr. has agreed to play for the Cleveland Indians for $3 million per year for the next 10 years. What table would you use to calculate the value of this contract in today's dollars?

A) Present value of an annuity
B) Present value of a single amount
C) Future value of an annuity
D) None of these