Deck 6: The Time Value of Money-Annuities and Other Topics

Question 1

What is the present value of $150 received at the beginning of each year for 16 years? The first payment is received today. Use a discount rate of 9%, and round your answer to the nearest $10.

A) $1,360
B) $1,480
C) $1,250
D) $1,210

Answer 1

A

Question 2

Ingrid Birdman can earn a nominal annual rate of return of 12%, compounded semiannually. If Ingrid made 40 consecutive semiannual deposits of $500 each, with the first deposit being made today, how much will she accumulate at the end of Year 20? Round off to the nearest $1.

A) $52,821
B) $57,901
C) $82,024
D) $64,132

Answer 2

C

Question 3

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 the nearest $1).

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

Answer 3

C

Question 4

It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account). Darwin will put $1,000 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 beginning of the 41st year? Assume that the account pays 12% interest compounded annually, and round to the nearest $1,000.

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

Question 5

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% interest per year, how many loan payments must the company make?

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

Question 6

Ordinary annuities assume that cash flows occur

A) at the beginning of a period.
B) at the end of a period.
C) annually
D) Both B and C

Question 7

What is the present value of an annuity of $27 received at the beginning of each year for the next six years? The first payment will be received today, and the discount rate is 10% (round to nearest $10).

A) $120
B) $130
C) $100
D) $110

Question 8

Charlie Stone wants to retire in 30 years, and he wants to have an annuity of $1,000 a year for 20 years after retirement. Charlie wants to receive the first annuity payment at the end of the 30th year. Using an interest rate of 10%, how much must Charlie invest today in order to have his retirement annuity (round to the nearest $10)?

A) $500
B) $490
C) $540
D) $570

Question 9

What is the present value of $300 received at the beginning of each year for five years? Assume that the first payment is not received until the beginning of the third year (thus the last payment is received at the beginning of the seventh year). Use a 10% discount rate, and round your answer to the nearest $1.00.

A) $1,137
B) $854
C) $940
D) $1,257

Question 10

A commercial bank will loan you $17,500 for two years to buy a car. The loan must be repaid in 24 equal monthly payments. The annual interest rate on the loan is 6% of the unpaid balance. What is the amount of the monthly payments?

A) $1,394.98
B) $688.11
C) $3779.39
D) $775.61

Question 11

You wish to borrow $2,000 to be repaid in 12 monthly installments of $170.30. The annual interest rate is

A) 24%.
B) 4%.
C) )04%.
D) 22%.

Question 12

As the number of monthly payments on a loan increases, the size of each payment ________ and the total interest paid over the life of the loan ________.

A) increases, decreases
B) decreases, stays the same
C) stays the same, decreases
D) decreases, increases

Question 13

Gina Dare, who wants to be a millionaire, plans to retire at the end of 40 years. Gina's plan is to invest her money by depositing into an IRA at the end of every year. What is the amount that she needs to deposit annually in order to accumulate $1,000,000? Assume that the account will earn an annual rate of 11.5%. Round off to the nearest $1.

A) $1,497
B) $5,281
C) $75
D) $3,622

Question 14

What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10). The discount rate is 13%. To solve this problem with a financial calculator, the correct choice is

A) N=7, i=13, PMT= 100, FV=0, solve for PV.
B) N=7, i=13, PV= 100, FV=0, solve for FV.
C) N=7, i=13, PMT= 100, FV=100, solve for PV.
D) N=7, i=.13, PMT= 100, FV=0, solve for PV.

Question 15

If you have $20,000 in an account earning 8% annually, what constant amount could you withdraw each year and have nothing remaining at the end of five years?

A) $3,525.62
B) $5,008.76
C) $3,408.88
D) $2,465.78

Question 16

Francis Peabody just won the $89,000,000 California State Lottery. The lottery offers the winner a choice of receiving the winnings in a lump sum or in 26 equal annual installments to be made at the beginning of each year. Assume that funds would be invested at 7.65%. Francis is trying to decide whether to take the lump sum or the annual installments. What is the amount of the lump sum that would be exactly equal to the present value of the annual installments? Round off to the nearest $1.

A) $89,000,000
B) $38,163,612
C) $13,092,576
D) $41,083,128

Question 17

If you invest $750 every six months at 8% compounded semi-annually, how much would you accumulate at the end of 10 years?

A) $10,065
B) $10,193
C) $22,334
D) $21,731

Question 18

What is the present value of $27 received at the end of each year for five years? Assume a discount rate of 9%. The first payment will be received one year from today (round to the nearest $1).

A) $42
B) $114
C) $88
D) $105

Question 19

What is the present value of $250 received at the beginning of each year for 21 years? Assume that the first payment is received today. Use a discount rate of 12%, and round your answer to the nearest $10.

A) $1,870
B) $2,090
C) $2,117
D) $3,243

Question 20

When comparing annuity due to ordinary annuities, annuity due annuities will have higher

A) present values.
B) annuity payments.
C) future values.
D) both A and C.
E) all of the above.

Question 21

Harold Hawkins bought a home for $320,000. He made a down payment of $45,000; the balance will be paid off over 30 years at a 6.775% rate of interest. How much will Harold's monthly payments be? Round off to the nearest $1.

A) $1,450
B) $1,788
C) $3,200
D) $1,682

Question 22

How much will you receive at the end of the 41st year (i.e., the first annuity payment)? Round to the nearest $100.

A) $2,567
B) $7,800
C) $10,666
D) $9,523

Question 23

To find the present value of an annuity due, one could

A) find the present value of an ordinary annuity and add one extra payment.
B) find the present value of an ordinary annuity but N=1 for the number of periods.
C) find the present value of an ordinary annuity and divide by 1+i.
D) find the present value of an ordinary annuity and multiply by 1+i.

Question 24

You have been accepted to study gourmet cooking at Le Cordon Bleu Culinary Institute in Paris, France. You will need $15,000 every six months (beginning six months from now) for the next three years to cover tuition and living expenses. Mom and Dad have agreed to pay for your education. They want to make one deposit now in a bank account earning 6% interest, compounded semiannually, so that you can withdraw $15,000 every six months for the next three years. How much must they deposit now?

A) $97,026
B) $73,760
C) $90,000
D) $81,258

Question 25

How much money must you pay into an account at the beginning of each of five years in order to have $5,000 at the end of the fifth year? Assume that the account pays 12% per year, and round to the nearest $1.00.

A) $703
B) $1,390
C) $1,550
D) $787

Question 26

You buy a race horse, which has a winning streak for four years, bringing in $500,000 per year, and then it dies of a heart attack. If you paid $1,518,675 for the horse four years ago, what was your annual return over this four-year period?

A) 8%
B) 33%
C) 18%
D) 12%

Question 27

You are considering a home loan with monthly payments at an annual percentage yield of 5.116%. What is the quoted rate of interest on the loan?

A) 4.5%
B) 4.75%
C) 5%
D) 6%

Question 28

Your investment goal is to have $3,000,000 in 40 years for retirement. You decide to invest in a mutual fund today that pays 12% per year compounded monthly. How much must you invest at the end of each month to meet your investment goal? Round to the nearest $1.

A) $245
B) $255
C) $285
D) $305
E) $315

Question 29

How much money will be in the account at the end of year 40 (round to the nearest $1.00?

A) $85,914
B) $76,709
C) $44,800
D) $93,000

Question 30

If you put $510 in a savings account at the beginning of each year for 30 years, how much money will be in the account at the end of the 30th year? Assume that the account earns 5%, and round to the nearest $100.

A) $33,300
B) $32,300
C) $33,900
D) None of the above

Question 31

How much money must you pay into an account at the beginning of each of 11 years in order to have $5,000 at the end of the 11th year? Assume that the account pays 8% per year, and round to the nearest $1.

A) $700
B) $257
C) $300
D) $278

Question 32

How much money must you pay into an account at the beginning of each of 20 years in order to have $10,000 at the end of the 20th year? Assume that the account pays 12% per annum, and round to the nearest $1.

A) $1,195
B) $111
C) $124
D) $139

Question 33

SellUCars, Inc. offers you a car loan at an annual interest rate of 8% compounded monthly. What is the annual percentage yield of the loan?

A) 8.00%
B) 8.24%
C) 8.30%
D) 8.44%

Question 34

A retirement plan guarantees to pay you or your estate a fixed amount for 20 years. At the time of retirement, you will have $31,360 to your credit in the plan. The plan anticipates earning 8% interest annually over the period you receive benefits. How much will your annual benefits be, assuming the first payment occurs one year from your retirement date?

A) $682
B) $6,272
C) $2,000
D) $3,194

Question 35

How much money must you pay into an account at the beginning of each of 30 years in order to have $10,000 at the end of the 30th year? Assume that the account pays 11% per annum, and round to the nearest $1.

A) $39
B) $45
C) $50
D) None of the above

Question 36

George and Laura will be retiring in four years and would like to buy a lake house. They estimate that they will need $550,000 at the end of four years to buy this house. They want to make four equal annual payments into an account at the end of each year. If they can earn 8% on their money, compounded annually, over the next four years, how much must they invest at the end of each year for the next four years to have accumulated $550,000 by retirement?

A) $137,500
B) $122,056
C) $113,015
D) $131,821

Question 37

You deposited $2,000 in a bank account paying 6% on January 1, 2004, and then you made $2,000 deposits on January 1 in 2005 and 2006. Which of the following expressions will calculate your bank balance just after the last payment was deposited?

A) FV = $2,000[1.06]-1 + $2,000[1.06]-2 + $2,000[1.06]-3
B) FV = $2,000[1.06]1 + $2,000[1.06]2 + $2,000[1.06]3
C) FV = $2,000[1.06]0 + $2,000[1.06]1 + $2,000[1.06]2
D) FV = $2,000[1.06]-0 + $2,000[1.06]-1 + $2,000[1.06]-2 + $1,000[1.06]-3

Question 38

If you put $10 in a savings account at the beginning of each year for 11 years, how much money will be in the account at the end of the 11th year? Assume that the account earns 11%, and round to the nearest $1.00.

A) $217
B) $241
C) $68.89
D) $76.47

Question 39

Horace and Myrtle want to buy a house. Their banker offered them a fully amortizing $95,000 loan at a 12% annual rate for 20 years. What will their monthly payment be if they make equal monthly installments over the next 20 years?

A) $1,046
B) $749
C) $1,722
D) $1,346

Question 40

Harry just bought a new four-wheel-drive Jeep Cherokee for his lumber business. The price of the vehicle was $35,000, of which he made a $5,000 down payment and took out an amortized loan for the rest. His local bank made the loan at 12% interest for five years. He is to pay back the principal and interest in five equal annual installments beginning one year from now. Determine the amount of Harry's annual payment.

A) $8,322
B) $9,600
C) $9,709
D) $6,720

Question 41

A friend of yours borrows $19,500 from the bank at 8% annually to be repaid in 10 equal annual end-of-year installments. The interest paid on this loan in year three is

A) $1,336.01.
B) $1,560.00.
C) $2,906.11.
D) $1,947.10.

Question 42

What is a series of equal payments to be received at the end of each period, for a finite period of time, called?

A) A perpetuity
B) An annuity due
C) A cash cow
D) An ordinary annuity

Question 43

What is the present value of an investment that pays $10,000 every year at year-end for the next five years and $15,000 every year at year-end for years six through 10? The annual rate of interest for the investment is 9%.

A) $125,000.00
B) $97,250.00
C) $135,173.00
D) $76,827.50

Question 44

You wish to purchase a condo at a cost of $175,000. You are able to make a down payment of $35,000 and will borrow $140,000 for 30 years at an interest rate of 7.25%. How much is your monthly payment? To solve this problems with an EXCEL spreadsheet, you would enter

A) =PMT(7.25/12,360,140000,0,1).
B) =PMT(.0725/12,360,140000,0,1).
C) =PMT(7.25,30,140000,0,1) /12.
D) =PMT(.0725/12,360,175000,0,1).

Question 45

You have borrowed $70,000 to buy a sports car. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the total amount of interest dollars you will pay the bank over the life of the loan. Round to the nearest dollar and assume end-of-month payments.

A) $47,451
B) $51,644
C) $54,776
D) $57,798

Question 46

A friend of yours plans to begin saving for retirement by depositing $2,000 at the end of each year for the next 25 years. If she can earn 10% annually on her investment, how much will she have accumulated at the end of 25 years?

A) $50,000
B) $196,692
C) $100,000
D) $216,361

Question 47

You have borrowed $70,000 to buy rental property. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the principal paid to the bank in month two of the loan. Assume end-of-period payments.

A) $184.01
B) $186.38
C) $188.46
D) $190.64
E) $192.73

Question 48

Edward Johnson decided to open up a Roth IRA. He will invest $1,800 per year for the next 35 years. Deposits to the Roth IRA will be made via a $150 payroll deduction at the end of each month. Assume that Edward will earn 8.75% annual interest compounded monthly over the life of the IRA. How much will he have at the end of 35 years?

A) $125,250
B) $250,321
C) $363,000
D) $414,405

Question 49

Suppose that you wish to save for your child's college education by opening up an educational IRA. You plan to deposit $100 per month into the IRA for the next 18 years. Assume that you will be able to earn 10%, compounded monthly, on your investment. How much will you have accumulated at the end of 18 years?

A) $21,600
B) $54,719
C) $33,548
D) $85,920
E) $60,056

Question 50

What is a series of equal payments for a finite period of time called?

A) A perpetuity
B) An axiom
C) A lump sum
D) An annuity

Question 51

If a loan of $10,000 is paid back in equal annual end-of-year payments of $2,570.69 during the next five years, what is the annual interest rate on the loan?

A) 2%
B) 5%
C) 9%
D) 12%

Question 52

Which of the following statements is true?

A) The future value of an annuity would be greater if funds are invested at the beginning of each period instead of at the end of each period.
B) An annuity is a series of equal payments that are made, or received, forever.
C) The effective annual rate (APR) of a loan is higher the less frequently payments are made.
D) The future value of an annuity would be greater if funds are invested at the end of each period rather than at the beginning of each period.

Question 53

If you have $375,000 in an account earning 9% annually, what constant amount could you withdraw each year and have nothing remaining at the end of 20 years?

A) $7,500
B) $18,750
C) $66,912
D) $5,575
E) $41,080

Question 54

You wish to borrow $12,000 to be repaid in 60 monthly installments of $257.93. The annual interest rate is

A) 10.50%.
B) 12.75%.
C) 15.25%.
D) 6.50%.
E) 8.80%.

Question 55

What is the value today of an investment that pays $500 every year at year-end during the next 15 years if the annual interest rate is 9%?

A) $4,030.50
B) $7,500.00
C) $3,500.00
D) $7,000.00

Question 56

How much would an investor be willing to pay today for an investment that returns $1,000 every year at year-end for five years if he wants to earn a 10% annual return on the investment?

A) $1,000
B) $3,791
C) $5,000
D) $7,700

Question 57

Congratulations. You just won the California State Lottery. The amount awarded is paid in 20 equal annual installments, at the beginning of each year. You can invest your money at 6.6%, compounded annually. You have calculated that the lottery is worth $20,975,400 today. How much was the amount awarded?

A) $75,310,294
B) $36,000,000
C) $81,047,770
D) $42,000,000

Question 58

Recently you borrowed money for a new car. The loan amount is $15,000 to be paid back in equal annual payments which begin today, and will continue to be payable at the beginning of each year for a total of five years. Interest on the loan is 8%. What is the amount of the loan payment?

A) $3,756.85
B) $4,200.00
C) $3,478.31
D) $3,000.00

Question 59

A friend of yours would like you to lend him $5,000 today to be paid back in 5 annual payments. What would be the equal annual end-of-year payment on this loan if you charge your friend 7% interest?

A) $869.45
B) $1,000.00
C) $1,219.51
D) $1,350.00

Question 60

How much must you deposit at the end of each of the next 10 years in a savings account paying 5% annually in order to have $10,000 saved by the end of the 10th year?

A) $1,000
B) $1,638
C) $1,500
D) $795

Question 61

Holding all other variables constant, payment per period for an annuity due will be higher than an ordinary annuity.

Question 62

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

Question 63

An annuity involves depositing or investing a single sum of money and allowing it to grow for a certain number of years.

Question 64

An amortized loan is a loan paid in unequal installments.

Question 65

What is a series of equal payments for an infinite period of time called?

A) A perpetuity
B) An axiom
C) A cash cow
D) An annuity

Question 66

When repaying an amortized loan, the interest payments increase over time.

Question 67

You are saving money to buy a house. You will need $7,473.50 to make the down payment. If you can deposit $500 per month in a savings account which pays 1% per month, how long will it take you to save the $7,473.50?

Question 68

You have just purchased a share of preferred stock for $50.00. The preferred stock pays an annual dividend of $5.50 per share forever. What is the rate of return on your investment?

A) 5.5%
B) 1.0%
C) 11.0 %
D) 22.2%

Question 69

If you have an opportunity cost of 10%, how much must you invest each year to have $4,000 accumulated in 10 years?

Question 70

You have borrowed $70,000 to buy a speed boat. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate, compounded monthly. Create an amortization schedule for the first two months of the loan.

Question 71

What is a series of equal payments to be received at the beginning of each period, for a finite period of time, called?

A) A perpetuity
B) An annuity due
C) A cash cow
D) A deferred annuity

Question 72

One characteristic of an annuity is that an equal sum of money is deposited or withdrawn each period.

Question 73

A loan amortization schedule provides a breakdown of loan payments into principal and interest payments.

Question 74

You have just received an endowment of $32,976. You plan to put the entire amount in an account earning 8 percent compounded annually and to withdraw $4000 at the end of each year. How many years can you continue to make the withdrawals?

Question 75

To repay a $2,000 loan from your bank, you promise to make equal payments every six months for the next five years totaling $3,116.20. What annual rate of interest will you be paying?

Question 76

You have a credit card with a balance of $18,000. The annual interest rate on the card is 18% compounded monthly, and the minimum payment is $400 per month. If you pay only the minimum payment each month and do not make any new charges on the card, how many years will it take for you to pay off the $18,000 balance?

Question 77

You have just purchased a car from Friendly Sam. The selling price of the car is $6,500. If you pay $500 down, then your monthly payments are $317.22. The annual interest rate is 24%. How many payments must you make?

Question 78

a.) If Sparco, Inc. deposits $150 at the end of each year for the next eight years in an account that pays 5% interest, how much money will Sparco have at the end of eight years?
b.) Suppose Sparco decides that they need to have $5,300 at the end of the eight years. How much will they have to deposit at the end of each year?

Question 79

We can use the present value of an annuity formula to calculate constant annual loan payments.

Question 80

The present value of a perpetuity decreases when the ________ decreases.

A) number of investment periods
B) annual discount rate
C) perpetuity payment
D) both B and C