Question 1

In three years you will begin receiving an annual payment of $600 that will be made for two years.If the annual interest rate is 12%,what will be the balance in your account at the end of the fourth year?
A) $2,025
B) $1,344
C) $1,272
D) $1,200
E) $1,260

Accepted Answer

FV = PMT × 11ea7fdb_fc16_f6c9_a768_2f12c5f15a8b_TB2902_11 FV = 600 × 11ea7fdb_fc16_f6ca_a768_65493259b01b_TB2902_11 = $1,272
Using a financial calculator:
N = 2, I/Y = 12, PV = 0, PMT = -600, cpt FV = $1,272

Question 2

You are saving for your child's university education.It is her 1st birthday today.She will start university just after her 19th birthday.You are going to save $2,000 per year each year starting today and ending on her 18th birthday.If you expect to earn a rate of 5% in the savings account,then how much will you have saved by her 19^th birthday? A) $56,264.77 B) $59,078.01 C) $61,078.01 D) $64,131,91 E) $54,264.77

Accepted Answer

FV = PMT × 11ea7fdb_fc18_0853_a768_233d7c19840b_TB2902_11 × 11ea7fdb_fc18_0854_a768_0156a93628fe_TB2902_11 FV = 2,000 × 11ea7fdb_fc18_0855_a768_31ce335b6775_TB2902_11 × 11ea7fdb_fc18_0856_a768_2f1001c9cb7a_TB2902_11 = $59,078.01
Using a financial calculator:
N = 18, I/Y = 5, PV = 0, PMT = -2,000, cpt FV = 56,264.77
56,264.77 × 1.05 = $59,078.01

Question 3

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 value 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.

Accepted Answer

The annuity due is always going to be worth more than the ordinary annuity, all else being equal.

Question 4

5-year regular annuity has a present value of $1,000,and if the interest rate is 10%,what is the amount of each annuity payment?
A) $240.42
B) $263.80
C) $300.20
D) $315.38
E) $346.87

Accepted Answer

PV = PMT × 11ea7fdb_fc18_7d8b_a768_8782f341a007_TB2902_11 PMT = PV / 11ea7fdb_fc18_7d8c_a768_33bb302a9fab_TB2902_11 PMT = 1,000 / 11ea7fdb_fc18_7d8d_a768_79fe91331fb0_TB2902_11 = $263.80
Using a financial calculator:
N = 5, I = 10, PV = -1,000, FV = 0, cpt PMT = $263.80

Question 5

An ordinary annuity may be defined as:
A) A series of equal payments made at regular intervals that are paid at the beginning of each period.
B) A series of payments, which may or may not be equal in value, that are received at regular intervals at the end of each period.
C) A series of equal payments made any time over the course of a year, extending for a period of several years.
D) Any series of payments that occur in the future.
E) A series of equal payments made at regular intervals that are received at the end of each period.

Accepted Answer

An ordinary annuity is a series of equal payments made at regular intervals that are received at the end of each period.

Question 6

Margaret plans to deposit $500 on the first day of each of the next five years,beginning today.If she earns 4% compounded annually,how much will she have at the end of five years?
A) $2,708.16
B) $2,816.49
C) $3,041.63
D) $1,560.80
E) $2,041.63

Accepted Answer

FV = PMT × 11ea7fdb_fc17_44ef_a768_43bece3d5e3d_TB2902_11 × 11ea7fdb_fc17_44f0_a768_81fc75428144_TB2902_11 FV = 500 × 11ea7fdb_fc17_44f1_a768_990ed4542c58_TB2902_11 × 11ea7fdb_fc17_44f2_a768_ef9a8684a73d_TB2902_11 = $2,816.49
Using a financial calculator:
N = 5, I/Y = 4, PV = 0, PMT = -500, cpt FV = 2,708.16
2,708.16 × 1.04 = $2,816.49

Question 7

If you buy a factory for $250,000 and the terms are 20% 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? (Round to the nearest whole dollar)
A) $20,593
B) $31,036
C) $24,829
D) $50,212
E) $6,667

Accepted Answer

Step 1 - Account for the down payment.
$250,000 × 20% = $50,000
$250,000 - 50,000 = $200,000 to be financed
Step 2 - Calculate the amount of each payment.
PV = PMT × 11ea7fdb_fc18_7d8e_a768_2d3afb8854f9_TB2902_11 PMT = PV / 11ea7fdb_fc18_a49f_a768_793c448dfe90_TB2902_11 PMT = 200,000 / 11ea7fdb_fc18_a4a0_a768_6da9c92c8fa6_TB2902_11 = $24,828.73
Using a financial calculator:
N = 30, I/Y = 12, PV = -200,000, FV = 0, cpt PMT = $24,828.73

Question 8

Indicate which of the following is true about annuities.
A) An ordinary annuity is an equal payment paid or received at the beginning of each period.
B) An annuity due is a payment paid or received at the beginning of each period, that increases by an equal amount each period.
C) An annuity due is an equal payment paid or received at the beginning of each period.
D) An ordinary annuity is an equal payment paid or received at the end of each period that increases by an equal amount each period.

Accepted Answer

An annuity due has equal payments, and they are made at the beginning of each period.

Question 9

Peter will receive $1,200 at the beginning of each of the next seven years.What is the future value of this annuity,assuming the interest rate is 9% compounded annually? (Round to the nearest whole dollar)
A) $1,200
B) $11,041
C) $12,034
D) $13,234
E) $8,400

Accepted Answer

FV = PMT × 11ea7fdb_fc17_9317_a768_693a0136f305_TB2902_11 × 11ea7fdb_fc17_9318_a768_4dc4013c0c18_TB2902_11 FV = 1,200 × 11ea7fdb_fc17_9319_a768_6b1b00e50bf3_TB2902_11 × 11ea7fdb_fc17_931a_a768_6355c3b5193b_TB2902_11 = $12,034.17
Using a financial calculator:
N = 7, I/Y = 9, PV = 0, PMT = -1200, cpt FV = 11,040.52
11,040.52 × 1.09 = $12,034.17

Question 10

In comparing an ordinary annuity and an annuity due,which of the following is true?
A) The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity.
B) The future value of an ordinary annuity is always greater than the future value of an otherwise identical annuity due.
C) The future value of an annuity due is always less than the future value of an otherwise identical ordinary annuity, since one less payment is received with an annuity due.
D) All things being equal, one would prefer to receive an ordinary annuity compared to an annuity due.

Accepted Answer

By receiving the payments sooner, the annuity due has a greater value than the ordinary annuity.

Question 11

An annuity in which payments are made at the beginning of each period is a(n):
A) Ordinary annuity
B) Annuity due
C) Annuity in arrears
D) Perpetuity

Accepted Answer

Payments from an annuity due are made at the beginning of the period.

Question 12

John wants to have $6,215 in 13 years to buy a Laser 2 sailboat with a spinnaker and trapeze.After he has owned the boat for 15 years he will need $2,500 for hull maintenance.How much must he deposit at the end of each year for the next 13 years to save enough money for the purchase and maintenance? His savings account pays 9%.
A) $300.67
B) $267.61
C) $213.02
D) $270.77
E) $211.68

Accepted Answer

Step 1 - Calculate the present value of $2,500 you will need in 15 years.
PV = 11ea7fdb_fc16_818f_a768_e10b473cc0a8_TB2902_11 PV = 11ea7fdb_fc16_a8a0_a768_9bbc2972d8ad_TB2902_11 = $686.35
Step 2 - Calculate how much you will need to invest for the future.
FV = PMT × 11ea7fdb_fc16_a8a1_a768_f755b09647b0_TB2902_11 PMT = FV / 11ea7fdb_fc16_a8a2_a768_03c7b7718979_TB2902_11 PMT = (6,215 + 686.35) / 11ea7fdb_fc16_a8a3_a768_91eb4b9c0149_TB2902_11 = $300.67
Using a financial calculator:
N = 13, I/Y = 9, PV = 0, FV = -6,901.35, cpt PMT = $300.67

Question 13

In future value or present value problems,unless stated otherwise,cash flows are assumed to be:
A) At the end of the time period.
B) At the beginning of the time period.
C) In the middle of the time period.
D) Spread out evenly over a time period.

Accepted Answer

Cash flows are always assumed to be received at the end of each time period.

Question 14

The Bentley Azure can be leased for four years for $0 down and 48 monthly payments of $4,000 (due at the beginning of each month).Today is the day that the first payment is due.If,instead,you save the payments in a bank account at the nominal annual rate of 7.5%,then how much money will you have at the end of the fourth year? (Round answer to the nearest whole dollar)
A) $224,498
B) $223,103
C) $221,984
D) $222,768
E) $223,326

Accepted Answer

FV = PMT × 11ea7fdb_fc18_2f67_a768_3726295565da_TB2902_11 × 11ea7fdb_fc18_2f68_a768_85c924476257_TB2902_11 FV = 4,000 × 11ea7fdb_fc18_2f69_a768_9d4f249429e1_TB2902_11 × 11ea7fdb_fc18_2f6a_a768_ed5073c7f854_TB2902_11 = $224,497.85
Using a financial calculator:
N = 18, I/Y = 5, PV = 0, PMT = -2,000, cpt FV = 223,103.46
223,103.46 × 1.00625 = $224,497.85

Question 15

Betty borrows $50,000 at 10 percent annually compounded interest to be repaid in four equal annual installments.The actual end of year loan payment is: (Round to the nearest whole dollar)
A) $10,774
B) $12,500
C) $14,340
D) $15,774

Accepted Answer

PV = PMT × 11ea7fdb_fc18_a4a1_a768_89c8dc14df37_TB2902_11 PMT = PV / 11ea7fdb_fc18_a4a2_a768_8de43a8908c0_TB2902_11 PMT = 50,000 / 11ea7fdb_fc18_cab3_a768_65b91a339106_TB2902_11 = $15,773.54
Using a financial calculator:
N = 4, I/Y = 10, PV = -50,000, FV = 0, cpt PMT = $15,773.54

Question 16

The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of next 10 years is: (Round to the nearest whole dollar)
A) $28,974
B) $31,291
C) $14,494
D) $13,420

Accepted Answer

FV = PMT × 11ea7fdb_fc17_ba2b_a768_531d4f2140f1_TB2902_11 × 11ea7fdb_fc17_ba2c_a768_71ca4de8a3e1_TB2902_11 FV = 2,000 × 11ea7fdb_fc17_ba2d_a768_89743e4c792b_TB2902_11 × 11ea7fdb_fc17_ba2e_a768_bb6ddc4e235a_TB2902_11 = $31,290.97
Using a financial calculator:
N = 10, I/Y = 8, PV = 0, PMT = -2,000, cpt FV = 28,973.12
28,973.12 × 1.08 = $31,290.97

Question 17

To pay for her college education,Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest.How much will Gina have in that account at the end of 8th year? (Round up to the nearest whole dollar amount)
A) $16,000
B) $17,920
C) $24,600
D) $27,552

Accepted Answer

FV = PMT × 11ea7fdb_fc17_6c03_a768_2ffd30b783ce_TB2902_11 × 11ea7fdb_fc17_6c04_a768_fbb1bc2c19dd_TB2902_11 FV = 2,000 × 11ea7fdb_fc17_6c05_a768_bd5f4141abad_TB2902_11 × 11ea7fdb_fc17_6c06_a768_01151ec1ff8b_TB2902_11 = $27,551.31
Using a financial calculator:
N = 8, I/Y = 12, PV = 0, PMT = -2,000, cpt FV = 24,599.38
24,599.38 × 1.12 = $27,551.31

Question 18

You want to buy a Nissan 300Z on your 27th birthday.You have priced these cars and found that they currently sell for $25,000.You believe that the price will increase by 10 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) $8,881.21
B) $4,540.14
C) $4,652.18
D) $4,239.56
E) $5,072.09

Accepted Answer

Step 1 - Calculate the future value of the car.
FV = PV × 11ea7fdb_fc16_cfb4_a768_63136d59b71e_TB2902_11 FV = 25,000 × (1.10 11ea7fdb_fc16_cfb5_a768_3ddd3a6982b7_TB2902_11 = $48,717.93
Step 2 - Use the future value of the car to calculate the amount that needs to be invested.
FV = PMT × 11ea7fdb_fc16_cfb6_a768_97e913a6b232_TB2902_11 PMT = FV / 11ea7fdb_fc16_cfb7_a768_b76443bee87f_TB2902_11 PMT = 48,717.93 / 11ea7fdb_fc16_cfb8_a768_97987e689dbd_TB2902_11 = $4,540.14
Using a financial calculator:
N = 7, I/Y = 14, PV = 0, FV = -48,717.93, cpt PMT = $4,540.14

Question 19

James plans to fund his individual retirement account,beginning today,with annual deposits of $2,000,which he will continue for the next 20 years.If he can earn an annual compound rate of 8 percent on his deposits,the amount in the account upon retirement would be: (Round to the nearest whole dollar)
A) $19,636
B) $91,524
C) $98,846
D) $21,207

Accepted Answer

FV = PMT × 11ea7fdb_fc17_e13f_a768_57ae9fd8a3d8_TB2902_11 × 11ea7fdb_fc17_e140_a768_c18ab8afb01b_TB2902_11 FV = 2,000 × 11ea7fdb_fc17_e141_a768_a5baa9dd5eb2_TB2902_11 × 11ea7fdb_fc17_e142_a768_cd68a2c8b25f_TB2902_11 = $98,845.84
Using a financial calculator:
N = 20, I/Y = 8, PV = 0, PMT = -2,000, cpt FV = 91,523.93
91,523.93 × 1.08 = $98,845.84

Question 20

What is the future value of an annuity due that pays $500 per year for each of the next three years if the interest rate is 6%?
A) $1,591.80
B) $1,687.31
C) $546.35
D) $2,123.25
E) $2,250.65

Accepted Answer

FV = PMT × 11ea7fdb_fc17_1ddb_a768_095a94ea69cc_TB2902_11 × 11ea7fdb_fc17_1ddc_a768_7521e59d91ad_TB2902_11 FV = 500 × 11ea7fdb_fc17_1ddd_a768_11e2a62fa5ee_TB2902_11 × 11ea7fdb_fc17_1dde_a768_09998bd55788_TB2902_11 = $1,687.31
Using a financial calculator:
N = 3, I/Y = 6, PV = 0, PMT = -500, cpt FV = 1,591.8
1,591.8 × 1.06 = $1,687.31

Quiz 4: Time Value of Money - Streams and Valuations

In three years you will begin receiving an annual payment of $600 that will be made for two years.If the annual interest rate is 12%,what will be the balance in your account at the end of the fourth year?

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?

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

An ordinary annuity may be defined as:

Margaret plans to deposit $500 on the first day of each of the next five years,beginning today.If she earns 4% compounded annually,how much will she have at the end of five years?

If you buy a factory for $250,000 and the terms are 20% 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? (Round to the nearest whole dollar)

Indicate which of the following is true about annuities.

Peter will receive $1,200 at the beginning of each of the next seven years.What is the future value of this annuity,assuming the interest rate is 9% compounded annually? (Round to the nearest whole dollar)

In comparing an ordinary annuity and an annuity due,which of the following is true?

An annuity in which payments are made at the beginning of each period is a(n) :

In future value or present value problems,unless stated otherwise,cash flows are assumed to be:

Betty borrows $50,000 at 10 percent annually compounded interest to be repaid in four equal annual installments.The actual end of year loan payment is: (Round to the nearest whole dollar)

The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of next 10 years is: (Round to the nearest whole dollar)

To pay for her college education,Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest.How much will Gina have in that account at the end of 8th year? (Round up to the nearest whole dollar amount)

What is the future value of an annuity due that pays $500 per year for each of the next three years if the interest rate is 6%?