Deck 5: The Time Value of Money

Question 1

$10,000 invested at 10% per year for 5 years earns interest equal to $6,105.10; therefore,$10,000 invested at 10% per year for 10 years will earn interest equal to $12,210.20 (2 times $6,105.10).

Answer 1

False

Question 2

A rational investor would prefer to receive $1,200 today rather than $100 per month for 12 months.

Answer 2

True

Question 3

An investment earning simple interest is preferred over an investment earning compound interest because the simplicity adds value.

Answer 3

False

Question 4

Inputs using an Excel spreadsheet are almost identical to those on a financial calculator,except the interest rate is entered either as a decimal (.05)or a whole number followed by a % sign (5%)rather than simply a whole number (5)as you would enter using a financial calculator.

Question 5

When solving time value of money problems on a financial calculator,you must select the "end mode" when you enter the final years cash flow.

Question 6

The present value of a single future sum

A) increases as the number of discount periods increases.
B) is generally larger than the future sum.
C) depends upon the number of discount periods.
D) increases as the discount rate increases.

Question 7

A timeline identifies the timing and amount of a stream of cash flows,along with the interest rate it earns.

Question 8

The time value of money is the opportunity cost of passing up the earning potential of a dollar today.

Question 9

Tim has $100 in a bank account paying 2% interest per year.At the end of 5 years,Tim's bank account balance will be $110 if interest is not compounded,but will be greater than $110 if interest is compounded.

Question 10

If you only earned interest on your initial investment,and not on previously earned interest,it would be called simple interest.

Question 11

Artificially low interest rates helped create the housing bubble because low interest rates (r value)create higher values (higher PVs).

Question 12

The same underlying formula is used for computing both the future value and present value.

Question 13

When solving a problem involving an annuity due,you must select the "beg" or beginning mode on your financial calculator.

Question 14

When using a financial calculator,cash outflows generally have to be entered as negative numbers,because a financial calculator sees money "leaving your hands."

Question 15

Suppose a corporation can change its depreciation method so that its tax payments will decrease by $1,000 this year but increase by $1,000 next year.

A) The change will have no impact on the value of the company because its cash flow over time will be the same.
B) The change will decrease the value of the company because investors don't like changes in accounting methods.
C) The change will decrease the value of the company because lower tax payments this year result from lower reported income.
D) The change will increase the value of the company because the value of the cash savings this year exceeds the cost of the cash payments next year.

Question 16

A car manufacturer offers either $2,000 cash back or zero percent financing for 5 years.A rational consumer will always take the cash back because money received today is worth more than money received in the future.

Question 17

Timelines are used for simple time value of money problems,but cannot be used for more complex problems.

Question 18

At an annual interest rate of 9%,an initial sum of money will double approximately every 8 years.

Question 19

The present value of a single future sum of money is inversely related to both the number of years until payment is received and the discount rate.

Question 20

When solving time value of money problems using Excel,the type = 0 variable means payments are made at the end of each period,and the type = 1 variable means payments are made at the beginning of each period.

Question 21

Ann deposited $1,000 in a bank account,and 10 years later she closes out the account,which is worth $2,000.What annual rate of interest has she earned over the 10 years?

A) 6.45%
B) 7.18%
C) 9.10%
D) 10.0%

Question 22

What is the present value of $15,500 to be received 12 years from today? Assume a discount rate of 7.5% compounded annually and round to the nearest $1.

A) $5,790
B) $6,508
C) $7,210
D) $9,010

Question 23

A zero coupon bond pays no annual coupon interest payments.When it matures at the end of 8 years it pays out $1,000.If investors wish to earn 7.5% per year on this bond investment,what is the current price of the bond?

A) $533
B) $561
C) $875
D) $840

Question 24

If the future value of an annuity is known,then the present value of the annuity can be found using the present value of a lump sum formula,even if the amount of each annuity payment is unknown.

Question 25

The present value of $1,000 to be received in 5 years is ________ if the discount rate is 7.8%.

A) $368
B) $494
C) $548
D) $687

Question 26

How much money must be put into a bank account yielding 3.5% (compounded annually)in order to have $1,250 at the end of 10 years (round to nearest $1)?

A) $921
B) $886
C) $843
D) $798

Question 27

Your parents are complaining about the price of items today compared to what they cost years ago.If an automobile that cost $12,000 in 1980 costs $40,000 in 2010,calculate the annual growth rate in the automobile's price.

Question 28

U)S.Savings Bonds are sold at a discount.The face value of the bond represents its value on its future maturity date.Therefore,

A) the current price of a $50 face value bond that matures in 10 years will be greater than the current price of a $50 face value bond that matures in 5 years.
B) the current price of a $50 face value bond that matures in 10 years will be less than the current price of a $50 face value bond that matures on 5 years.
C) the current prices of all $50 face value bonds will be the same, regardless of their maturity dates because they will all be worth $50 in the future.
D) the current price of a $50 face value bond will be higher if interest rates increase.

Question 29

You decide you want your child to be a millionaire.You have a son today and you deposit $15,000 in an investment account that earns 9% per year.The money in the account will be distributed to your son whenever the total reaches $1,000,000.How old will your son be when he gets the money (rounded to the nearest year)?

A) 82 years
B) 74 years
C) 60 years
D) 49 years

Question 30

Bill wants to buy a new boat in 7 years.He expects the new boat will cost $28,000.Bill has $18,000 in an investment account today.What rate of return must Bill earn on his investments to be able to buy the boat on time?

Question 31

You borrow $30,000 and agree to pay it off with one lump sum payment of $40,000 in 6 years.What annual rate of interest will you be charged?

Question 32

If the future value of annuity A is greater than the future value of annuity B,then the present value of annuity A must also be greater than the present value of annuity B.

Question 33

How much money do I need to place into a bank account that pays a 6% rate in order to have $500 at the end of 7 years?

A) $332.53
B) $751.82
C) $463.77
D) $629.52

Question 34

The future value of an annuity will increase if the interest rate goes up,but the present value of the same annuity will decrease as the interest rate goes up.

Question 35

Bill and Cathy will be retiring in fifteen years and would like to buy an Italian villa.The villa costs $500,000 today,and housing prices in Italy are expected to increase by 6% per year.Bill and Cathy want to make fifteen equal annual payments into an account,starting today,so there will be enough money to purchase the villa in fifteen years.If the account earns 10% per year,what is the amount of each deposit?

A) $79,885
B) $72,623
C) $34,286
D) $32,947

Question 36

You want to travel to Europe to visit relatives when you graduate from college three years from now.The trip is expected to cost a total of $10,000 at that time.Your parents have deposited $5,000 for you in a CD paying 6% interest annually,maturing three years from now.Aunt Hilda has agreed to finance the balance.If you are going to put Aunt Hilda's gift in an investment earning 10% over the next three years,how much must she deposit now,so you can visit your relatives at the end of three years?

A) $3,757
B) $3,039
C) $5,801
D) $3,345

Question 37

At what rate must $500 be compounded annually for it to grow to $1,079.46 in 10 years?

A) 6 percent
B) 5 percent
C) 7 percent
D) 8 percent

Question 38

Assuming two investments have equal lives,a high discount rate tends to favor

A) the investment with large cash flow early.
B) the investment with large cash flow late.
C) the investment with even cash flow.
D) neither investment since they have equal lives.

Question 39

Which of the following conclusions would be true if you earn a higher rate of return on your investments?

A) The greater the present value would be for any lump sum you would receive in the future.
B) The lower the present value would be for any lump sum you would receive in the future.
C) Your rate of return would not have any effect on the present value of any sum to be received in the future.
D) The greater the present value would be for any annuity you would receive in the future.

Question 40

You just invested $50,000 into an account that earns 7 percent compounded annually.At the end of each year you can withdraw $4,971.How many years can you continue to make the withdrawals?

Question 41

If the interest rate is positive,then the future value of an annuity due will be greater than the future value of an ordinary annuity.

Question 42

You charged $1,000 on your credit card for Christmas presents.Your credit card company charges you 26% annual interest,compounded monthly.If you make the minimum payments of $25 per month,how long will it take ( to the nearest month)to pay off your balance?

A) 94 months
B) 79 months
C) 54 months
D) 40 months

Question 43

Two brothers each open IRAs in 2009 and plan to invest $3,000 per year for the next 30 years.John makes his first deposit on January 1,2009,and will make all future deposits on the first day of the year.Bill makes his first deposit on December 31,2009,and will continue to make his annual deposits on the last day of each year.At the end of 30 years,the difference in the value of the IRAs (rounded to the nearest dollar),assuming an interest rate of 7% per year,will be

A) $19,837.
B) $12,456.
C) $6,300.
D) $210.

Question 44

You have the choice of two equally risk annuities,each paying $5,000 per year for 8 years.One is an annuity due and the other is an ordinary annuity.If you are going to be receiving the annuity payments,which annuity would you choose to maximize your wealth?

A) The annuity due
B) The ordinary annuity
C) Since we don't know the interest rate, we can't find the value of the annuities and hence we cannot tell which one is better.
D) Either one because they have the same present value.

Question 45

Bill borrowed $100,000 today that he must repay in 15 annual end-of-year installments of $10,000.What annual interest rate is Bill paying on his loan?

A) 2.222%
B) 3.333%
C) 5.556%
D) 33.33%

Question 46

Joe borrowed $10,000 at 10% per year and promised to pay it back in equal annual installments at the end of each of the next 5 years.Joe's payment will be $2,100 [($10,000/5)+ ($10,000 × 10%).

Question 47

John has to pay $1,000 per month for his mortgage for another 5 years,but he is considering paying the mortgage off in one lump sum.John cannot calculate the present value of the payments using the annuity formulas because his payments are monthly and not once per year.

Question 48

Assume you are to receive a 10-year annuity with annual payments of $100.The first payment will be received at the end of Year 1,and the last payment will be received at the end of Year 10.You will invest each payment in an account that pays 9 percent compounded annually.Although the annuity payments stop at the end of year 10,you will not withdraw any money from the account until 20 years from today,and the account will continue to earn 9% for the entire 20-year period.What will be the value in your account at the end of Year 20 (rounded to the nearest dollar)?

A) $38,359
B) $35,967
C) $28,000
D) $19,000

Question 49

The value of a bond investment,which provides fixed interest payments,will increase when discounted at a 8% rate rather than at a 11% rate.

Question 50

When repaying an amortized loan,the interest payments increase over time due to the compounding process.

Question 51

The future value of a 10-year ordinary annuity is twice as much as the future value of an otherwise identical 5-year annuity.

Question 52

Bill saves $3,000 per year in his IRA starting at age 25 and continuing to age 65,when he retires.The amount Bill has in his IRA at age 65 can be characterized as the future value of an annuity.

Question 53

If the interest rate is positive,then the present value of an annuity due will be less than the present value of an ordinary annuity.

Question 54

To evaluate or compare investment proposals,we must adjust the value of all cash flows to a common date.

Question 55

You deposit $5,000 per year at the end of each of the next 25 years into an account that pays 8% compounded annually.How much could you withdraw at the end of each of the 20 years following your last deposit if all withdrawals are the same dollar amount? (The twenty-fifth and last deposit is made at the beginning of the 20-year period.The first withdrawal is made at the end of the first year in the 20-year period.)

A) $18,276
B) $27,832
C) $37,230
D) $43,289

Question 56

An example of an annuity is the interest received from bonds.

Question 57

If the interest rate is positive,a six-year ordinary annuity of $500 per year must have a present value over $3,000.

Question 58

The future value of an annuity due is greater than the future value of an otherwise identical ordinary annuity.

Question 59

The present value of an annuity increases as the discount rate increases.

Question 60

The present value of a deferred annuity .

Question 61

Auto Loans R Them loans you $24,000 for four years to buy a car.The loan must be repaid in 48 equal monthly payments.The annual interest rate on the loan is 9 percent.What is the monthly payment?

A) $500.92
B) $543.79
C) $563.82
D) $597.24

Question 62

You inherit $300,000 from your parents and want to use the money to supplement your retirement.You receive the money on your 65^th birthday,the day you retire.You want to withdraw equal amounts at the end of each of the next 20 years.What constant amount can you withdraw each year and have nothing remaining at the end of 20 years if you are earning 7% interest per year?

A) $15,000
B) $28,318
C) $33,574
D) $39,113

Question 63

It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account).Darwin will put $1000 into the account on December 31st of this year and at the end of each year for the following 39 years (40 years total).How much money will Darwin have in his account at the end of the 40^th year? Assume that the account pays 12% interest compounded annually and round to nearest $1000.

A) $93,000
B) $766,000
C) $767,000
D) $850,000

Question 64

You decide to borrow $250,000 to build a new home.The bank charges an interest rate of 8% compounded monthly.If you pay back the loan over 30 years,what will your monthly payments be (rounded to the nearest dollar)?

A) $1,123
B) $1,237
C) $1,687
D) $1,834

Question 65

You can buy a $50 savings bond today for $25 and redeem the bond in 10 years for its full face value of $50.You could also put your money in a money market account that pays 7% interest per year.Which option is better,assuming they are of equal risk?

A) The money market account is better because it pays more interest.
B) The money market account is better because it requires a smaller investment.
C) The savings bond is better because it earns a higher interest rate.
D) The money market and savings bond both earn 7% interest, so they are equal in value.

Question 66

You estimate you'll need $200,000 per year for 25 years starting on your 65^th birthday to live on during your retirement.Today is your 50^th birthday and you want to make equal deposits into an account paying 9% interest per year,the first deposit today and the last deposit on your 64^th birthday.How much must each deposit be (rounded to the nearest $10)?

A) $99,920
B) $85,840
C) $61,385
D) $49,380

Question 67

What is the present value of an annuity of $4,000 received at the beginning of each year for the next eight years? The first payment will be received today,and the discount rate is 9% (round to nearest $1).

A) $36,288
B) $35,712
C) $25,699
D) $24,132

Question 68

It is your 5^th birthday today.You have a trust fund with $50,000 that is earning 8% per year.You expect to withdraw $20,000 per year for 4 years starting on your 21^st birthday for graduate school.How much money will be left in the trust fund after your last withdrawal (rounded to the nearest $10)?

A) $125,660
B) $135,780
C) $91,30
D) You will not have enough money to pay for graduate school.

Question 69

You borrow $25,000 to be repaid in 12 monthly installments of $2,292.00.The annual interest rate is closest to

A) 1.5 percent.
B) 12 percent.
C) 18 percent.
D) 24 percent.

Question 70

What is the present value of an annuity of $12 received at the end of each year for seven years? Assume a discount rate of 11%.The first payment will be received one year from today (round to nearest $1).

A) $25
B) $40
C) $57
D) $118

Question 71

Your grandparents deposit $2,000 each year on your birthday,starting the day you are born,in an account that pays 7% interest compounded annually.How much will you have in the account on your 21st birthday,just after your grandparents make their deposit?

A) $101,802
B) $98,016
C) $86,058
D) $79,640

Question 72

Your daughter is born today and you want her to be a millionaire by the time she is 35 years old.You open an investment account that promises to pay 12% per year.How much money must you deposit each year,starting on her 1st birthday and ending on her 35th birthday,so your daughter will have $1,000,000 by her 35th birthday?

A) $2,317
B) $3,455
C) $5,777
D) $9,450

Question 73

A financial advisor tells you that you can make your child a millionaire if you just start saving early.You decide to put an equal amount each year into an investment account that earns 7.5% interest per year,starting on the day your child is born.How much would you need to invest each year (rounded to the nearest dollar)to accumulate a million for your child by the time he is 35 years old? (Your last deposit will be made on his 34^th birthday.)

A) $6,525
B) $7,910
C) $12,500
D) $20,347

Question 74

Your company has received a $50,000 loan from an industrial finance company.The annual payments are $6,202.70.If the company is paying 9 percent interest per year,how many loan payments must the company make?

A) 15
B) 13
C) 12
D) 19

Question 75

You inherit $300,000 from your parents and want to use the money to supplement your retirement.You receive the money on your 65^th birthday,the day you retire.You want to withdraw equal amounts at the end of each of the next 20 years.What constant amount can you withdraw each month and have nothing remaining at the end of 20 years if you are earning 7% interest compounded monthly?

A) $1,200
B) $1,829
C) $2,326
D) $2,943

Question 76

You are 21 years old today.Your grandparents set up a trust fund that will pay you $25,000 per year for 20 years,starting on your 65^th birthday to supplement your retirement.If the trust can earn 7.5% per year,how much will your grandparents need to put in the trust fund today (rounded to the nearest ten dollars)?

A) $11,370
B) $22,310
C) $5,250
D) $17,450

Question 77

You own an ordinary annuity contract that will pay you $3,000 per year for 12 years.You need money to pay back a loan in 6 years,and you are afraid if you get the annuity payments annually you will spend the money and not be able to pay back your loan.You decide to sell your annuity for a lump sum of cash to be paid to you five years from today.If the interest rate is 8%,what is the equivalent value of your 12-year annuity if paid in one lump sum five years from today?

A) $22,008
B) $18,000
C) $35,876
D) $38,880

Question 78

Charlie wants to retire in 15 years,and he wants to have an annuity of $50,000 a year for 20 years after retirement.Charlie wants to receive the first annuity payment the day he retires.Using an interest rate of 8%,how much must Charlie invest today in order to have his retirement annuity (round to nearest $10).

A) $167,130
B) $200,450
C) $256,890
D) $315,240

Question 79

A 65 year-old man is retiring and can take either $500,000 in cash or an ordinary annuity that promises to pay him $50,000 per year for as long as he lives.Which of the following statements is most correct?

A) Because of the time value of money, the man will always be better off taking the $500,000 up front.
B) The higher the interest rate, the more likely the man will prefer the $500,000 lump sum.
C) If the man expects to live more than 10 years, then he will prefer the annuity.
D) If the man is certain the company will not default on its future payments, he should select the $50,000 per year.

Question 80

A deferred annuity will pay you $500 at the end of each year for 10 years,however the first payment will not be made until three years from today (payments will be made at the end of years 3 through 12).What amount will you have to deposit today to fund this deferred annuity? Use an 8% discount rate and round your answer to the nearest $100.

A) $2,200
B) $2,400
C) $2,900
D) $3,400