Deck 4: Time Value of Money

Question 1

Which of the following statements best describes time lines?

A) A time line is not meaningful unless all cash flows occur annually.
B) Time lines are useful for visualizing complex problems prior to doing actual calculations.
C) Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly.
D) Time lines can be constructed only for annuities where the payments occur at the ends of the periods, i.e., for ordinary annuities.

Answer 1

B

Question 2

Midway through the life of an amortized loan, the percentage of the payment that represents interest is equal to the percentage that represents principal repayment. This is true regardless of the original life of the loan.

Answer 2

False

Question 3

Which of the following statements is correct?

A) If you have a series of cash flows, all of which are positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0.
B) To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the PV of the negative CFs. This is, essentially, a trial-and- error procedure that is easy with a computer or financial calculator but quite difficult otherwise.
C) If you solve for I and get a negative number, then you must have made a mistake.
D) If CF0 is positive and all the other CFs are negative, then you cannot solve for I.

Answer 3

B

Question 4

When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage declines in the loan's later years.

Question 5

Which of the following bank accounts has the highest effective annual return?

A) an account that pays 8% nominal interest with monthly compounding
B) an account that pays 7% nominal interest with daily (365-day) compounding
C) an account that pays 7% nominal interest with monthly compounding
D) an account that pays 8% nominal interest with daily (365-day) compounding

Question 6

The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be
received at some future date.

Question 7

The present value of a future sum decreases as either the discount rate or the number of periods per year increases.

Question 8

Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is correct?

A) The periodic rate of interest is 1.5% and the effective rate of interest is 3%.
B) The periodic rate of interest is 6% and the effective rate of interest is greater than 6%.
C) The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.
D) The periodic rate of interest is 3% and the effective rate of interest is 6%.

Question 9

Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value.

Question 10

If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.

Question 11

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan).

Question 12

Which of the following statements is INCORRECT?

A) A time line is meaningful only if all cash flows occur annually.
B) Time lines can be constructed even in situations where some of the cash flows occur annually but others occur quarterly.
C) Time lines can be constructed for annuities where the payments occur at either the beginning or the end of periods.
D) The cash flows shown on a time line can be in the form of annuity payments, but they can also be uneven amounts.

Question 13

Suppose an investor plans to invest a given sum of money. She can earn an effective annual rate of 5% on Security A, while Security B will provide an effective annual rate of 12%. Within 11 years' time, the compounded value of Security B will be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Question 14

All other factors held constant, the present value of a given annual annuity decreases as the number of discounting periods per year increases.

Question 15

You are analyzing the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?

A) The discount rate increases.
B) The riskiness of the investment's cash flows decreases.
C) The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.
D) The discount rate decreases.

Question 16

If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series.

Question 17

One potential benefit from starting to invest early for retirement is that the investor can expect greater benefits from the compounding of interest.

Question 18

Which of the following statements best describes annuities?

A) The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
B) If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.
C) The cash flows for an annuity due must all occur at the ends of the periods.
D) The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month.

Question 19

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.

Question 20

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal.

Question 21

You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?

A) $2,245.08
B) $2,363.24
C) $2,481.41
D) $2,605.48

Question 22

Which of the following statements is INCORRECT?

A) The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.
B) If a loan has a nominal annual rate of 8%, then the effective rate can never be less than 8%.
C) If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be the same.
D) An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is less than 6%.

Question 23

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is correct?

A) The monthly payments will decline over time.
B) A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment.
C) The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%.
D) Exactly 10% of the first monthly payment represents interest.

Question 24

Which of the following statements regarding a 15-year (180-month) $125,000 fixed-rate mortgage is INCORRECT? (Ignore all taxes and transactions costs.)

A) The remaining balance after 3 years will be $125,000 less the total amount of interest paid during the first 36 months.
B) Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant.
C) The proportion of the monthly payment that goes toward repayment of principal will be higher 10 years from now than it will be the first year.
D) The outstanding balance gets paid off at a faster rate in the later years of a loan's life.

Question 25

How many years would it take $50 to triple if it were invested in a bank that pays 3.8% per year?

A) 25.26
B) 26.58
C) 27.98
D) 29.46

Question 26

Suppose a Government of Canada bond will pay $2,500 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today?

A) $1,928.78
B) $2,030.30
C) $2,131.81
D) $2,238.40

Question 27

Which of the following investments will have the HIGHEST FUTURE VALUE at the end of 10 years? Assume that the effective annual rate for all investments is the same.

A) Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
B) Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
C) Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
D) Investment D pays $2,500 at the end of 10 years (a total of one payment).

Question 28

A Canada government bond promises to pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is correct?

A) The periodic interest rate is greater than 3%.
B) The periodic rate is less than 3%.
C) The present value would be greater if the lump sum were discounted back for more periods.
D) The present value of the $1,000 would be smaller if interest were compounded monthly rather than semiannually.

Question 29

What would the future value of $125 be after 8 years at 8.5% compound interest?

A) $205.83
B) $216.67
C) $228.07
D) $240.08

Question 30

Last year Toto Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later?

A) $271.74
B) $286.05
C) $301.10
D) $316.16

Question 31

Suppose a Government of Canada bond promises to pay $1,000 five years from now. If the going interest rate on 5-year government bonds is 5.5%, how much is the bond worth today?

A) $765.13
B) $803.39
C) $843.56
D) $885.74

Question 32

A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is correct?

A) The annual payments would be larger if the interest rate were lower.
B) If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan.
C) The proportion of each payment that represents interest as opposed to repayment of principal would be lower if the interest rate were lower.
D) The last payment would have a higher proportion of interest than the first payment.

Question 33

You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest?

A) Bank 1; 6.0% with monthly compounding
B) Bank 2; 6.0% with annual compounding
C) Bank 3; 6.0% with quarterly compounding
D) Bank 4; 6.0% with daily (365-day) compounding

Question 34

How much would $5,000 due in 50 years be worth today if the discount rate were 7.5%?

A) $109.51
B) $115.27
C) $127.72
D) $134.45

Question 35

Which of the following statements is correct, assuming positive interest rates and other things held constant?

A) A 5-year, $250 annuity due will have a lower present value than a similar ordinary annuity.
B) A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.
C) A typical investment's nominal interest rate will always be equal to or less than its effective annual rate.
D) If an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%.

Question 36

How much would $1, growing at 3.5% per year, be worth after 75 years?

A) $12.54
B) $13.20
C) $13.86
D) $14.55

Question 37

You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is correct?

A) The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE.
B) The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.
C) The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
D) The present value of DUE exceeds the present value of ORD, and the future value of DUE also
Exceeds the future value of ORD.

Question 38

Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures?

A) $1,781.53
B) $1,870.61
C) $1,964.14
D) $2,062.34

Question 39

Ten years ago, Levin Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in Levin's earnings per share (EPS) over the 10-year period?

A) 15.97%
B) 16.77%
C) 17.61%
D) 18.49%

Question 40

Suppose the Government of Canada offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?

A) 4.37%
B) 4.86%
C) 5.40%
D) 6.00%

Question 41

You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning 1 year from today. You plan to deposit the funds in a mutual fund that you expect to return 8.5% per year. Under these conditions, how much will you have just after you make the fifth deposit, 5 years from now?

A) $18,368.66
B) $19,287.09
C) $20,251.44
D) $21,264.02

Question 42

You have a chance to buy an annuity that pays $550 at the BEGINNING of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

A) $1,412.84
B) $1,487.20
C) $1,565.48
D) $1,643.75

Question 43

You plan to invest in securities that pay 9.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment account to grow to $9,140.20?

A) 4.59
B) 5.10
C) 6.30
D) 7.00

Question 44

What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?

A) $8,956.56
B) $9,427.96
C) $9,924.17
D) $10,446.50

Question 45

You own an oil well that will pay you $30,000 per year for 10 years, with the first payment being made today. If you think a fair return on the well is 8.5%, how much should you ask for if you decide to sell it?

A) $202,893
B) $213,572
C) $224,250
D) $235,463

Question 46

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the BEGINNING of each of the next 25 years and end up with zero in the account?

A) $28,243.21
B) $29,729.70
C) $31,294.42
D) $32,859.14

Question 47

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and to be able to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account?

A) $28,843.38
B) $30,361.46
C) $31,959.43
D) $33,641.50

Question 48

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?

A) $28,532.45
B) $29,959.08
C) $31,457.03
D) $33,029.88

Question 49

Your aunt is about to retire, and she wants to buy an annuity that will supplement her income by $65,000 per year for 25 years, beginning a year from today. The going rate on such annuities is 6.25%. How much would it cost her to buy such an annuity today?

A) $770,963.15
B) $811,540.16
C) $852,117.17
D) $894,723.02

Question 50

Your aunt is about to retire, and she wants to buy an annuity that will provide her with $65,000 of income a year for 25 years, with the first payment coming IMMEDIATELY. The going rate on such annuities is 6.25%. How much would it cost her to buy the annuity today?

A) $739,281.38
B) $778,190.93
C) $819,148.35
D) $862,261.42

Question 51

You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning 1 year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the third deposit, 3 years from now?

A) $11,973.07
B) $12,603.23
C) $13,266.56
D) $13,929.88

Question 52

What is the PV of an annuity due with 10 payments of $2,700 at an interest rate of 6.5%?

A) $20,671.48
B) $21,705.06
C) $22,790.31
D) $23,929.82

Question 53

Last year Mason Corp's earnings per share were $2.50, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Mason's EPS to double?

A) 5.86
B) 6.52
C) 7.24
D) 8.04

Question 54

You want to go to Europe 5 years from now, and you can save $3,100 per year, BEGINNING IMMEDIATELY. You plan to deposit the funds in a mutual fund that you expect to return 8.5% per year. Under these conditions, how much will you have just after you make the fifth deposit, 5 years from now?

A) $17,986.82
B) $18,933.49
C) $19,929.99
D) $20,926.49

Question 55

You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, BEGINNING IMMEDIATELY. You will make three deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today?

A) $13,956.42
B) $14,654.24
C) $15,386.95
D) $16,156.30

Question 56

You have a chance to buy an annuity that pays $1,200 at the end of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

A) $2,775.77
B) $2,921.86
C) $3,075.64
D) $3,237.52

Question 57

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 6.5%?

A) $16,641.51
B) $17,517.38
C) $18,439.35
D) $19,409.84

Question 58

Your uncle has $375,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning at the end of this year. How many years will it take to exhaust his funds, i.e., run the account down to zero?

A) 22.50
B) 23.63
C) 24.81
D) 26.05

Question 59

Your uncle has $500,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $40,000 at the BEGINNING of each year, beginning immediately. How many years will it take to exhaust his funds, i.e., run the account down to zero?

A) 24.38
B) 25.66
C) 27.01
D) 28.44

Question 60

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the BEGINNING of each of the next 20 years?

A) $22,598.63
B) $23,788.03
C) $25,040.03
D) $26,357.92

Question 61

An investment costs $725 and is expected to produce cash flows of $75 at the end of Year 1, $100 at the end of Year 2, $85 at the end of Year 3, and $625 at the end of Year 4. What rate of return would you earn if you bought this investment?

A) 5.19%
B) 5.46%
C) 5.75%
D) 6.05%

Question 62

What is the present value of the following cash flow stream at an interest rate of 12.0% per year: $0 at Time 0; $1,500 at the end of Year 1; $3,000 at the end of Year 2; $4,500 at the end of Year 3; and
$6,000 at the end of Year 4?

A) $10,209.64
B) $10,746.99
C) $11,284.34
D) $11,848.55

Question 63

What annual payment would you have to receive in order to earn a 7.5% rate of return on a perpetuity that has a cost of $1,250?

A) $89.06
B) $93.75
C) $98.44
D) $103.36

Question 64

What's the present value of $1,500 discounted back 5 years if the appropriate interest rate is 6%, compounded semiannually?

A) $956.95
B) $1,007.32
C) $1,060.33
D) $1,116.14

Question 65

You agree to make 24 deposits of $500 at the BEGINNING of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?

A) 7.62%
B) 8.00%
C) 8.40%
D) 8.82%

Question 66

Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the END of each year, beginning at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

A) 14.96
B) 15.71
C) 16.49
D) 17.32

Question 67

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded monthly?

A) $1,922.11
B) $2,023.28
C) $2,124.44
D) $2,230.66

Question 68

An investment costs $1,000 (CF at t = 0) and is expected to produce cash flows of $75 at the end of each of the next 5 years, then an additional lump sum payment of $1,000 at the end of the 5th year. What is the expected rate of return on this investment?

A) 6.77%
B) 7.13%
C) 7.50%
D) 7.88%

Question 69

At a rate of 6.5%, what is the future value of the following cash flow stream: $0 at Time 0; $75 at the end of Year 1; $225 at the end of Year 2; $0 at the end of Year 3; and $300 at the end of Year 4?

A) $526.01
B) $553.69
C) $613.51
D) $645.80

Question 70

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

A) $4,750.00
B) $5,000.00
C) $5,250.00
D) $5,512.50

Question 71

Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the BEGINNING of each year, beginning immediately. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

A) 11.98
B) 12.61
C) 13.27
D) 14.63

Question 72

Your friend just won the lottery. She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming 1 year from today. What rate of return is built into the annuity?

A) 2.79%
B) 3.10%
C) 3.44%
D) 3.79%

Question 73

What's the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly?

A) $969.34
B) $1,020.36
C) $1,074.06
D) $1,130.59

Question 74

What is the present value of the following cash flow stream if the interest rate is 6.0% per year: 0 at Time 0; $1,000 at the end of Year 1; and $2,000 at the end of Years 2, 3, and 4?

A) $5,986.81
B) $6,286.16
C) $6,600.46
D) $6,930.4

Question 75

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?

A) $1,819.33
B) $1,915.08
C) $2,015.87
D) $2,116.67

Question 76

At a rate of 6.25%, what is the present value of the following cash flow stream: $0 at Time 0; $75 at the end of Year 1; $225 at the end of Year 2; $0 at the end of Year 3; and $300 at the end of Year 4?

A) $433.23
B) $456.03
C) $480.03
D) $505.30

Question 77

An investment promises the following cash flow stream: $750 at Time 0; $2,450 at the end of Year 1 (or at t = 1); $3,175 at the end of Year 2; and $4,400 at the end of Year 3. At a discount rate of 8.0%, what is the present value of the cash flow stream?

A) $7,916.51
B) $8,333.17
C) $8,771.76
D) $9,233.43

Question 78

You just won the lottery, and you have a choice between receiving $3,500,000 today or a 10-year annuity of $500,000, with the first payment coming 1 year from today. What rate of return is built into the annuity?

A) 6.72%
B) 7.07%
C) 7.43%
D) 7.80%

Question 79

What's the rate of return you would earn if you paid $950 for a perpetuity that pays $85 per year?

A) 6.52%
B) 7.25%
C) 8.95%
D) 9.84%

Question 80

Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. Your uncle offers to give you $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment?

A) 6.85%
B) 7.21%
C) 7.59%
D) 8.41%