Deck 9: Time Value of Money

Question 1

Which of the following statements is correct?

A) Cash flow time lines are helpful graphical displays for situations involving simple annual interest but are not useful when time periods are more frequent than annual.
B) The future value of an annuity due is equal to the future value of an otherwise identical regular annuity with interest compounded on each payment for one additional period.
C) There is no precise method of calculating either present values or future values when fractional time periods are involved.We must instead use rough approximations.
D) The terminal value of a stream of uneven cash flows is found by simply summing up all the cash flows.
E) The annual percentage rate (APR) cannot be equivalent to the effective annual rate (EAR).

Answer 1

The future value of an annuity due is equal to the future value of an otherwise identical regular annuity with interest compounded on each payment for one additional period.

Question 2

At an effective annual interest rate of 20 percent, how many years will it take a given amount to triple in value? (Round to the closest year.)

A) 5
B) 8
C) 6
D) 10
E) 9

Answer 2

6

Question 3

You deposited $1,000 in a savings account that pays 8 percent interest, compounded quarterly, planning to use it to finish your last year in college.Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account.How much money will you receive?

A) $1,171
B) $1,126
C) $1,082
D) $1,163
E) $1,008

Answer 3

$1,126

Question 4

What is the present value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate?

A) $670.43
B) $842.91
C) $1,169.56
D) $1,348.48
E) $1,522.64

Question 5

Which of the following statements is correct?

A) Simple rates can't be used in present value or future value calculations because they fail to account for compounding effects.
B) The periodic interest rate can be used directly in calculations as long as the number of payments per year is greater than or equal to the number of compounding periods per year.
C) In all cases where interest is added or payments are made more frequently than annually, the periodic rate is less than the annual rate.
D) Generally, the APR is greater than the EAR as a result of compounding effects.
E) If the compounding period is semiannual then the periodic rate will equal the effective annual rate divided by two.

Question 6

You have determined the profitability of a planned project by finding the present value of all the cash flows form that project.Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?

A) The discount rate decreases.
B) The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same.
C) The discount rate increases.
D) Answers b and c above.
E) Answers a and b above.

Question 7

Which of the following statements is most correct?

A) If annual compounding is used, the effective annual rate equals the simple rate.
B) If annual compounding is used, the effective annual rate equals the periodic rate.
C) If a loan has a 12 percent simple rate with semiannual compounding, its effective annual rate is equal to 11/66 percent.
D) Both answers a and b are correct.
E) Both answers a and c are correct.

Question 8

Supposed someone offered you the choice of two equally risky annuities, each paying $10,000 per year for five years.One is an ordinary (or deferred) annuity, the other is an annuity due.Which of the following statements is most correct?

A) The present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due.
B) The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the ordinary annuity.
C) The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity.
D) If interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same.
E) Both answers a and d are correct.

Question 9

Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years.One is an annuity due, while the other is a regular (or deferred) annuity.If you are a rational wealth-maximizing investor which annuity would you choose?

A) The annuity due.
B) The deferred annuity.
C) Either one, because as the problem is set up, they have the same present value.
D) Without information about the appropriate interest rate, we cannot find the values of the two annuities; hence we cannot tell which is better.
E) The annuity due; however, if the payments on both were doubled to $10,000, the deferred annuity would be preferred.

Question 10

Which of the following statements is correct?

A) The PV of an ordinary annuity will be larger than the PV of an annuity due, other things held constant.
B) The effective annual rate will always be greater than the simple rate except in situations where the periodic rate is equal to the simple rate.
C) If you were borrowing money from a bank, and the simple interest rate was 10 percent, you would be better off if the bank used daily rather than quarterly compounding.
D) If you were borrowing money from a bank, and the simple interest rate was 10 percent, daily compounding, you would be better off if the bank used a 365-day year rather than a 360-day year.
E) $100 placed in a bank account which pays 6 percent will double faster if the bank pays interest annually rather than daily.

Question 11

Which of the following statements is correct?

A) If a bank uses quarterly compounding for saving accounts, the simple rate will be greater than the effective annual rate.
B) The present value of a future sum increases as the simple interest rate increases or the number of discount periods per year decreases.
C) The present value of a future sum increases as either the simple interest rate or the number of discount periods per year increases.
D) The present value of a future sum decreases as either the simple interest rate or the number of discount periods per year increases.
E) All of the above statements are false.

Question 12

If you presently have $6,000 invested at a rate of 15 percent, how many years will it take for your investment to triple? (Round up to obtain a whole number of years if necessary.)

A) 2 years
B) 4 years
C) 6 years
D) 8 years
E) 10 years

Question 13

Which of the following statements is false?

A) If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series.
B) To increase present consumption beyond present income normally requires either the payment of interest or else an opportunity cost of interest foregone.
C) Disregarding risk, if money has time value, it is impossible for the present value of a given sum to be greater than its future value.
D) Disregarding risk, if the present value of a sum is equal to its future value, either r = 0 or t = 0.
E) Each of the above statements is true.

Question 14

What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate?

A) $670.44
B) $842.91
C) $1,169.56
D) $1,522.64
E) $1,348.48

Question 15

Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will

A) Be higher.
B) Be lower.
C) Stay the same.
D) Cannot tell.
E) Be variable.

Question 16

A recent advertisement in the financial section of a magazine carried the following claim: "Invest your money with us at 14 percent, compounded annually, and we guarantee to double your money sooner than you imagine." Ignoring taxes, how long would it take to double your money at a simple rate of 14 percent, compounded annually?

A) Approximately 3.5 years
B) Approximately 5 years
C) Exactly 7 years
D) Approximately 10 years
E) Exactly 14 years

Question 17

Which of the following statements is correct?

A) Other things held constant, an increase in the number of discounting periods per year increases the present value of a given annual annuity.
B) Other things held constant, an increase in the number of discounting periods per year increases the present value of a lump sum to be received in the future.
C) The payment made each period under an amortized loan is constant, and it consists of some interest and some principal.The later we are is the loan's life, the smaller the interest portion of the payment.
D) There is an inverse relationship between the present value interest factor of an annuity and the future value interest factor of an annuity, (i.e., one is the reciprocal of the other).
E) Each of the above statements is true.

Question 18

Which of the following statements is most correct?

A) The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent.
B) If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent simple, or quoted, rate but with semiannual payments, rather than at a 10.1 percent simple rate with annual payments.However, as a borrower you should prefer the annual payment loan.
C) The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero.
D) Statements a, b, and c are all true.
E) Only statements b and c are true.

Question 19

As the discount rate increases without limit, the present value of the future cash inflows

A) Gets larger without limit.
B) Stays unchanged.
C) Approaches zero.
D) Gets smaller without limit, i.e., approaches minus infinity.
E) Goes to e^rn.

Question 20

A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments.Given the following facts, 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 5 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 5-year amortization plan.
C) The last payment would have a higher proportion of interest than the first payment.
D) The proportion of interest versus principal repayment would be the same for each of the 5 payments.
E) The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher.

Question 21

You will receive a $100 annual perpetuity starting at Year 0, a $300 annual perpetuity with the first payment at the end of Year 5, and a $200 semiannual perpetuity ^1/2 − 1.0 = 7%.)

A) $2,091.86
B) $2,785.14
C) $4,213.51
D) Infinite; the future value of any perpetuity is infinite.
E) Cannot determine the value since some payments are received annually and some semiannually.

Question 22

If $100 is placed in an account that earns a simple 4 percent, compounded quarterly, what will it be worth in 5 years?

A) $122.02
B) $105.10
C) $135.41
D) $120.90
E) $117.48

Question 23

Assume that you can invest to earn a stated annual rate of return of 12 percent, but where interest is compounded semiannually.If you make 20 consecutive semiannual deposits of $500 each, with the first deposit being made today, what will your balance be at the end of Year 20?

A) $52,821.19
B) $57,900.83
C) $58,988.19
D) $62,527.47
E) $64,131.50

Question 24

South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments of $2,504.56.What annual interest rate is the company paying?

A) 7%
B) 8%
C) 9%
D) 10%
E) 11%

Question 25

If a 5-year regular annuity has a present value of $1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment?

A) $240.42
B) $263.80
C) $300.20
D) $315.38
E) $346.87

Question 26

Gomez Electronics needs to arrange financing for its expansion program.Bank A offers to lend Gomez the required funds on a loan where interest must be paid monthly, and the quoted rate is 8 percent.Bank B will charge 9 percent, with interest due at the end of the year.What is the difference in the effective annual rates charged by the two banks?

A) 0.25%
B) 0.50%
C) 0.70%
D) 1.00%
E) 1.25%

Question 27

Suppose the present value of a 2-year ordinary annuity is $100.If the discount rate is 10 percent, what must be the annual cash flow?

A) $65.45
B) $82.64
C) $57.62
D) $53.78
E) $79.22

Question 28

Your subscription to Jogger's World Monthly is about to run out and you have the choice of renewing it by sending in the $10 a year regular rate or of getting a lifetime subscription to the magazine by paying $100.Your opportunity cost is 7 percent.How many years would you have to live to make the lifetime subscription the better buy? Payments for the regular subscription are made at the beginning of each year.(Round up if necessary to obtain a whole number of years.)

A) 15 years
B) 10 years
C) 18 years
D) 7 years
E) 8 years.

Question 29

Assume you are to receive a 20-year annuity with annual payments of $50.The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 20.You will invest each payment in an account that pays 10 percent.What will be the value in your account at the end of Year 30?

A) $6,354.81
B) $7,427.83
C) $7,922.33
D) $8,591.00
E) $6,752.46

Question 30

At an inflation rate of 9 percent, the purchasing power of $1 would be cut in half in 8.04 years.How long to the nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4%?

A) 12 years
B) 15 years
C) 18 years
D) 20 years
E) 23 years

Question 31

You expect to receive $1,000 at the end of each of the next 3 years.You will deposit these payments into an account which pays 10 percent compounded semiannually.What is the future value of these payments, that is, the value at the end of the third year?

A) $3,000
B) $3,310
C) $3,318
D) $3,401
E) $3,438

Question 32

As the winning contestant in a television game show, you are considering the prizes to be awarded.You must indicate to the sponsor which of the following two choices you prefer, assuming you want to maximize your wealth.Assume it is now January 1, and there is no danger whatever that the sponsor won't pay off. Which one would you choose?

A) Choice 1
B) Choice 2
C) Choice 1, if the payments were made at the end of the year.
D) The choice would depend on how soon you need the money.
E) Either one, since they have the same present value.

Question 33

On January 1, 2006, a graduate student developed a 5-year financial plan which would provide enough money at the end of her graduate work (January 1, 2011) to open a business of her own.Her plan was to deposit $8,000 per year for 5 years, starting immediately, into an account paying 10 percent compounded annually.Her activities proceeded according to plan except that at the end of her third year (1/1/09) she withdrew $5,000 to take a Caribbean cruise, at the end of the fourth year (1/1/10) she withdrew $5,000 to buy a used Prelude, and at the end of the fifth year (1/1/11) she had to withdraw $5,000 to pay to have her dissertation typed.Her account, at the end of the fifth year, was less than the amount she had originally planned on by how much?

A) $15,373
B) $16,550
C) $32,290
D) $38,352
E) $13,975

Question 34

An investor is considering the purchase of 20 acres of land.An analysis indicates that if the land is used for cattle grazing, it will produce a cash flow of $1,000 per year indefinitely.If the investor requires a return of 10 percent on investments of this type, what is the most he or she should be willing to pay for the land?

A) $1,000
B) $10,000
C) $100,000
D) $150,000
E) $1,000,000

Question 35

Assume that, to help build your nest-egg, you made two deposits of $100, one on January 1, 2014, and one on July 1, 2014, in a savings account that paid 10 percent compounded semiannually.On January 1, 2015, the bank increased the interest rate paid on savings accounts to 12 percent, annual compounding.Then you made a third $100 deposit on April 1, 2015.How much should there be in your account on January 1, 2016?

A) $353.08
B) $349.95
C) $355.27
D) $362.10
E) $338.43

Question 36

In 1981 the average tuition for one year at a certain state school was $1,800.Thirty years later, in 2011, the average cost was $13,700.What was the growth rate in tuition over the 30-year period?

A) 12%
B) 9%
C) 6%
D) 7%
E) 8%

Question 37

You want to buy a Nissan 300ZX on your 27th birthday.You have priced these cars and found that they currently sell for $30,000.You believe that the price will increase by 5 percent per year until you are ready to buy.You can presently invest to earn 14 percent.If you just turned 20 years old, how much must you invest at the end of each of the next 7 years to be able to purchase the Nissan in 7 years?

A) $4,945.57
B) $3,933.93
C) $7,714.72
D) $3,450.82
E) $6,030.43

Question 38

Assume that you will receive $2,000 a year in Years 1 through 5, $3,000 a year in Years 6 through 8, and $4,000 in Year 9, with all cash flows to be received at the end of the year.If you require a 14 percent rate of return, what is the present value of these cash flows?

A) $9,851
B) $13,250
C) $11,714
D) $15,129
E) $17,353

Question 39

You have the opportunity to buy a perpetuity which pays $1,000 annually.Your required rate of return on this investment is 15 percent.You should be essentially indifferent to buying or not buying the investment if it were offered at a price of

A) $5,000.00
B) $6,000.00
C) $6,666.67
D) $7,500.00
E) $8,728.50

Question 40

You just graduated, and you plan to work for 10 years and then to leave for the Australian "Outback" bush country.You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years.These savings cash flows will start one year from now.In addition, your family has just given you a $5,000 graduation gift.If you put the gift now, and your future savings when they start, into an account which pays 8 percent compounded annually, what will your financial "stake" be when you leave for Australia 10 years from now?

A)
$21,432
B)
$28,393
C)
$16,651
D)
$31,148
E)
$20,000

Question 41

Suppose you put $100 into a savings account today, the account pays a simple annual interest rate of 6 percent, but compounded semiannually, and you withdraw $100 after 6 months.What would your ending balance be 20 years after the initial $100 deposit was made?

A) $226.20
B) $115.35
C) $62.91
D) $9.50
E) $3.00

Question 42

You have just taken out an installment loan for $100,000.Assume that the loan will be repaid in 12 equal monthly installments of $9,456 and that the first payment will be due one month from today.How much of your third monthly payment will go toward the repayment of principal?

A) $7,757.22
B) $6,359.12
C) $7,212.50
D) $7,925.88
E) $8,333.33

Question 43

You want to borrow $1,000 from a friend for one year, and you propose to pay her $1,120 at the end of the year.She agrees to lend you the $1,000, but she wants you to pay her $10 of interest at the end of each of the first 11 months plus $1,010 at the end of the 12th month.How much higher is the effective annual rate under your friend's proposal than under your proposal?

A) 0.00%
B) 0.45%
C) 0.68%
D) 0.89%
E) 1.00%

Question 44

Your parents start saving for your sister's college education.She will begin college when she turns age 18 and will need $4,000 at that time and at the end of each of the following 3 years.They will make a deposit at the end of this year in an account which pays 6 percent compounded annually, and an identical deposit at the end of each year with the last deposit occurring when she turns age 18.If an annual deposit of $1,484 will allow them to reach their goal, how old is your sister now?

A) 13
B) 8
C) 14
D) 12
E) 10

Question 45

Assume that your required rate of return is 12 percent and you are given the following stream of cash flows: If payments are made at the end of each period, what is the present value of the cash flow stream?

A) $66,909
B) $57,323
C) $61,815
D) $52,345
E) $62,029

Question 46

Your mother's employer offers a tax-deferred retirement plan (a 401-b plan, which was authorized by Congress to encourage savings) which would permit her to invest, tax-free until she retires, up to 15 percent of her salary.Once you are out of school (one year from today), she figures she can save $1,000 every 6 months, or $2,000 per year.The insurance company which manages the retirement fund promises to pay a stated (or simple) rate of 12 percent per year, but with quarterly compounding.If your mother invests $1,000 each six months, starting six months after you graduate (or 18 months from today), how much will she have 5 years from now, assuming the last payment is made at the end of Year 5? (Hint: She will make a total of 8 payments.)

A) $12,300
B) $12,462
C) $9,897
D) $9,929
E) $10,000

Question 47

If it were evaluated with an interest rate of 0 percent, a 10-year regular annuity would have a present value of $3,755.50.If the future (compounded) value of this annuity, evaluated at Year 10, is $5,440.22, what effective annual interest rate must the analyst be using to find the future value?

A) 7%
B) 8%
C) 9%
D) 10%
E) 11%

Question 48

You are currently at time period 0, and you will receive the first payment on an annual payment annuity of $100 in perpetuity at the end of this year.Six full years from now you will receive the first payment on an additional $150 in perpetuity, and at the end of time period 10 you will receive the first payment on an additional $200 in perpetuity.If you require a 10 percent rate of return, what is the combined present value of these three perpetuities?

A) $2,349.50
B) $2,526.85
C) $2,685.42
D) $2,779.58
E) $2,975.40

Question 49

The present value (t = 0) of the following cash flow stream is $5,979.04 when discounted at 12 percent annually.What is the value of the missing (t = 2) cash flow?

A) $2,000
B) $2,391
C) $3,000
D) $3,391
E) $4,237

Question 50

Find the present value of an income stream which has a negative flow of $100 per year for 3 years, a positive flow of $200 in the 4th year, and a positive flow of $300 per year in Years 5 through 8.The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years.Thus, a cash flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years.All payments occur at year-end.

A) $528.21
B) $1,329.00
C) $792.49
D) $1,046.41
E) $875.18

Question 51

Express Airlines is considering the purchase of an aircraft to supplement its current fleet.In estimating the impact of adding this aircraft to the fleet, management has developed the following expected cash flows: If the discount rate is 10 percent, what is the present value of these estimated flows?

A) $379,080
B) $224,211
C) $189,760
D) $154,869
E) $199,000

Question 52

Drexel Corporation has been enjoying a phenomenal rate of growth since its inception one year ago.Currently, its assets total $100,000.If growth continues at the current rate of 12 percent compounded quarterly, what will total assets be in 2¹/₂ years?

A) $142,571
B) $126,678
C) $148,016
D) $136,855
E) $134,392

Question 53

Steaks Galore needs to arrange financing for its expansion program.One bank offers to lend the required $1,000,000 on a loan which requires interest to be paid at the end of each quarter.The quoted rate is 10 percent, and the principal must be repaid at the end of the year.A second lender offers 9 percent, daily compounding (365-day year), with interest and principal due at the end of the year.What is the difference in the effective annual rates (EFF%) charged by the two banks?

A) 0.31%
B) 0.53%
C) 0.75%
D) 0.96%
E) 1.25%

Question 54

Bank One currently charges a 10 percent simple rate on a car loan where the interest is compounded semiannually.Bank Two offers a car loan where the interest is compounded quarterly.What simple rate would Bank Two have to charge in order to earn the same effective annual rate that is earned by Bank One?

A) 9.25%
B) 9.88%
C) 10.00%
D) 10.25%
E) 10.42%

Question 55

Assume that you are graduating, that you plan to work for 4 years, and then to go to law school for 3 years.Right now, going to law school would require $17,000 per year (for tuition, books, living expenses, etc.), but you expect this cost to rise by 8 percent per year in all future years.You now have $25,000 invested in an investment account which pays a simple annual rate of 9 percent, quarterly compounding, and you expect that rate of return to continue into the future.You want to maintain the same standard of living while in law school that $17,000 per year would currently provide.You plan to save and to make 4 equal payments (deposits) which will be added to your account at the end of each of the next 4 years; these new deposits will earn the same rate as your investment account currently earns.How large must each of the 4 payments be in order to permit you to make 3 withdrawals, at the beginning of each of your 3 years in law school? (Note: (1) The first payment is made a year from today and the last payment 4 years from today, (2) the first withdrawal is made 4 years from today, and (3) the withdrawals will not be of a constant amount.)

A) $13,242.67
B) $6,562.13
C) $10,440.00
D) $7,153.56
E) $14,922.85

Question 56

A project with a 3-year life has the following probability distributions for possible end of year cash flows in each of the next three years: Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows.(Hint: Find the expected cash flow in each year, then evaluate those cash flows.)

A) $1,204.95
B) $835.42
C) $1,519.21
D) $1,580.00
E) $1,347.61

Question 57

You are given the following cash flow information.The appropriate discount rate is 12 percent for Years 1−5 and 10 percent for Years 6−10.Payments are received at the end of the year. What should you be willing to pay right now to receive the income stream above?

A) $166,866
B) $158,791
C) $225,000
D) $125,870
E) $198,433

Question 58

You are given the following cash flows.What is the present value (t = 0) if the discount rate is 12 percent?

A) $3,277
B) $4,804
C) $5,302
D) $4,289
E) $2,804

Question 59

In its first year of operations, 2001, the Gourmet Cheese Shoppe had earnings per share (EPS) of $0.26.Four years later, in 2005, EPS was up to $0.38, and 7 years after that, in 2012, EPS was up to $0.535.It appears that the first 4 years represented a supernormal growth situation and since then a more normal growth rate has been sustained.What are the rates of growth for the earlier period and for the later period?

A) 6%; 5%
B) 6%; 3%
C) 10%; 8%
D) 10%; 5%
E) 12%; 7%

Question 60

If you buy a factory for $250,000 and the terms are 20 percent down, the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance, what are the 30 equal annual payments?

A) $20,593
B) $31,036
C) $24,829
D) $50,212
E) $6,667

Question 61

You have just taken out a 30-year mortgage on your new home for $120,000.This mortgage is to be repaid in 360 equal monthly installments.If the stated (simple) annual interest rate is 14.75 percent, what is the amount of each of the monthly installments?

A) $1,515.00
B) $1,472.38
C) $1,493.41
D) $1,522.85
E) $1,440.92

Question 62

Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years.He wants a retirement income which has, in the first year, the same purchasing power as $40,000 has today.However, his retirement income will be of a fixed amount, so his real income will decline over time.His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments.Inflation is expected to be constant at 5 percent.Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future.How much must he save each year, starting today, to meet his retirement goals?

A) $1,863
B) $2,034
C) $2,716
D) $5,350
E) $6,102

Question 63

You have just taken out a 30-year, $120,000 mortgage on your new home.This mortgage is to be repaid in 360 equal end-of-month installments.If each of the monthly installments is $1,500, what is the effective annual interest rate on this mortgage?

A) 15.87%
B) 14.75%
C) 13.38%
D) 16.25%
E) 16.49%

Question 64

Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years.Suppose your father wants to have a real income of $40,000 in today's dollars in each year after he retires.His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments.Inflation is expected to be constant at 5 percent.Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future.How much must he save each year, starting today, to meet his retirement goals?

A) $1,863
B) $2,034
C) $2,716
D) $5,350
E) $6,102

Question 65

Assume that you inherited some money.A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling some securities which call for four payments, $50 at the end of each of the next 3 years, plus a payment of $1,050 at the end of Year 4.Your friend says she can get you some of these securities at a cost of $900 each.Your money is now invested in a bank that pays an 8 percent simple (quoted) interest rate, but with quarterly compounding.You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit.You must calculate the value of the securities to decide whether they are a good investment.What is their present value to you?

A) $1,000
B) $866
C) $1,050
D) $901
E) $893

Question 66

Your lease calls for payments of $500 at the end of each month for the next 12 months.Now your landlord offers you a new 1-year lease which calls for zero rent for 3 months, then rental payments of $700 at the end of each month for the next 9 months.You keep your money in a bank time deposit that pays a simple annual rate of 5 percent.By what amount would your net worth change if you accept the new lease? (Hint: Your return per month is 5%/12 = 0.4166667%.)

A) −$509.81
B) −$253.62
C) +$125.30
D) +$253.62
E) +$509.81

Question 67

You plan to invest $2,500 in a money market account which will pay an annual stated (simple) interest rate of 8.75 percent, but which compounds interest on a weekly basis.If you leave this money on deposit for one year (52 weeks), what will be your ending balance when you close the account?

A) $2,583.28
B) $2,611.72
C) $2,681.00
D) $2,703.46
E) $2,728.50

Question 68

You are currently saving for your child's college education.The current cost of college is $10,000 a year.You expect that college costs will continue to increase at a rate of 5 percent a year.Your child is scheduled to begin attending a four-year college 10 years from now .You currently have $25,000 in an account which earns 6 percent after taxes.You would like to have all of the necessary savings by the time your child enters college, and you would like to contribute a constant amount at the beginning of each of the next 10 years in order to provide the necessary amount.(You want to make 10 equal contributions starting in Year 0 and ending at Year 9.) How much should you contribute to the account each year in order to fully provide for your child's education?

A) $1,133.16
B) $1,393.42
C) $1,477.02
D) $1,507.81
E) $1,622.33

Question 69

You have a 30-year mortgage with a simple annual interest rate of 8.5 percent.The monthly payment is $1,000.What percentage of your total payments over the first three years goes toward the repayment of principal?

A) 1.50%
B) 3.42%
C) 5.23%
D) 6.75%
E) 8.94%

Question 70

Your client just turned 75 years old and plans on retiring in 10 years on her 85th birthday.She is saving money today for her retirement and is establishing a retirement account with your office.She would like to withdraw money from her retirement account on her birthday each year until she dies.She would ideally like to withdraw $50,000 on her 85th birthday, and increase her withdrawals 10 percent a year through her 89th birthday (i.e., she would like to withdraw $73,205 on her 89th birthday).She plans to die on her 90th birthday, at which time she would like to leave $200,000 to her descendants.Your client currently has $100,000.You estimate that the money in the retirement account will earn 8 percent a year over the next 15 years.Your client plans to contribute an equal amount of money each year until her retirement.Her first contribution will come in one year; her tenth and final contribution will come in ten years (on her 85th birthday).How much should she contribute each year in order to meet her objectives?

A) $12,401.59
B) $12,998.63
C) $13,243.18
D) $13,759.44
E) $14,021.53

Question 71

Assume that you just had a child, and you are now planning for her college education.You would like to make 43 equal payments over the next 21 years (the first payment to be made immediately, all other payments to be made at 6-month intervals, with the final payment to be made at her 21st birthday) so that you will be able to cover her expected expenses while in school.You expect to pay expenses on her 18th, 19th, 20th, and 21st birthdays.Assume that the current (time period 0) annual cost of college is $6,000, that you expect annual inflation to be 8 percent for the next 5 years, and then 5 percent thereafter.If you expect to be able to earn a return of 4 percent every 6 months on your investments (a simple rate of 8 percent with semiannual compounding), what will be the amount of each of the 43 payments?

A) $705.86
B) $731.93
C) $692.15
D) $650.46
E) $785.72

Question 72

Your company is planning to borrow $1,000,000 on a 5-year, 15 percent, annual payment, fully amortized term loan.What fraction of the payment made at the end of the second year will represent repayment of principal?

A) 29.83%
B) 57.18%
C) 35.02%
D) 64.45%
E) 72.36%

Question 73

Your company must make payments of $100,000 each year for 10 years, with the first payment to be made 10 years from today.To prepare for these payments, your company must make 10 equal annual deposits into an account which pays a simple interest rate of 7 percent, daily compounding (360-day year).Funds will remain in the account during both the accumulation period (the first 10 years) and the distribution period (the last 10 years), and the same interest rate will be earned throughout the entire 20 years.The first deposit will be made immediately.How large must each deposit be?

A) $47,821.11
B) $49,661.86
C) $51,234.67
D) $52,497.33
E) $53,262.39

Question 74

A bank pays a quoted annual (simple) interest rate of 8 percent.However, it pays interest (compounds) daily using a 365-day year.What is the effective annual rate of return?

A) 7.86%
B) 7.54%
C) 8.57%
D) 8.33%
E) 9.21%

Question 75

The Desai Company just borrowed $1,000,000 for 3 years at a quoted rate of 8 percent, quarterly compounding.The loan is to be amortized in end-of-quarter payments over its 3-year life.How much interest (in dollars) will your company have to pay during the second quarter?

A) $15,675.19
B) $18,508.81
C) $21,205.33
D) $24,678.89
E) $28,111.66

Question 76

You have just borrowed $20,000 to buy a new car.The loan agreement calls for 60 monthly payments of $444.89 each to begin one month from today.If the interest is compounded monthly, then what is the effective annual rate on this loan?

A) 12.68%
B) 14.12%
C) 12.00%
D) 13.25%
E) 15.08%

Question 77

You can deposit your savings at the Darlington National Bank, which offers to pay 12.6 percent interest compounded monthly, or at the Bartlett Bank, which will pay interest of 11.5 percent compounded daily.(Assume 365 days in a year.) Which bank offers the higher effective annual rate?

A) Darlington National Bank.
B) Bartlett Bank.
C) Both banks offer the same effective rate.
D) Cannot be determined from the information provided.
E) Workable only if the banks use the same compounding period.

Question 78

Bank A offers a 2-year certificate of deposit (CD) that pays 10 percent compounded annually.Bank B offers a 2-year CD that is compounded semi-annually.The CDs have identical risk.What is the stated, or simple, rate that Bank B would have to offer to make you indifferent between the two investments?

A) 9.67%
B) 9.76%
C) 9.83%
D) 9.87%
E) 9.93%

Question 79

You have just purchased a life insurance policy that requires you to make 40 semiannual payments of $350 each, where the first payment is due in 6 months.The insurance company has guaranteed that these payments will be invested to earn you an effective annual rate of 8.16 percent, although interest is to be compounded semiannually.At the end of 20 years (40 payments), the policy will mature.The insurance company will pay out the proceeds of this policy to you in 10 equal annual payments, with the first payment to be made one year after the policy matures.If the effective interest rate remains at 8.16 percent, how much will you receive during each of the 10 years?

A) $6,113.20
B) $5,244.62
C) $5,792.21
D) $4,992.39
E) $4,723.81

Question 80

You are considering an investment in a 40-year security.The security will pay $25 a year at the end of each of the first three years.The security will then pay $30 a year at the end of each of the next 20 years.The simple interest rate is assumed to be 8 percent, and the current price (present value) of the security is $360.39.Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (i.e., for 17 years)?

A) $35
B) $38
C) $40
D) $45
E) $50