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Postal Express is considering the purchase of a new sorting machine.
The sales quote consists of quarterly payments of $37,200 for five years at 7.6 percent interest.
What is the purchase price?
 
A. $621,380.92
B. $614,184.40
C. $687,418.22
D. $774,311.28
E. $836,267.35
 
PV = $37,200 × (1 - {1 / [1 + (.076 / 4)]20}) / (.076 / 4) = $614,184.40
   
Today, you are purchasing a 20-year, 6 percent annuity at a cost of $48,350.
The annuity will pay annual payments starting one year from today.
What is the amount of each payment?
 
A. $4,511.08
B. $4,215.37
C. $2,754.40
D. $4,013.20
E. $5,208.19
 
PV = $48,350 = C × {1 - [1 / (1 + .06)20]} / .06 C = $4,215.37
   
You will receive annual payments of $800 at the end of each year for 12 years.
The first payment will be received in Year 3. What is the present value of these payments if the discount rate is 7 percent?
 
A. $5,465.20
B. $6,018.52
C. $6,299.80
D. $5,549.96
E. $6,856.60
 
PV2 = $800× ({1 - [1 / (1 + .07)12]} / .07) × (1 + .07) = $6,354.15
PV0 = $6,354.15 / (1 + .07)2 = $5,549.96
   
You want to purchase a new condominium that costs $287,500.
Your plan is to pay 25 percent down in cash and finance the balance over 15 years at 3.75 percent.
What will be your monthly mortgage payment including principal and interest?
 
A. $1,568.07
B. $1,333.33
C. $1,708.16
D. $1,221.43
E. $1,406.11
 
Amount financed = (1 - .25) ×$287,500 = $215,625
PV = $215,625 = C × (1 - {1 / [1 + (.0375 / 12)]180}) / (.0375 / 12) C = $1,568.07
   
What is the effective annual rate of 8.25 percent compounded quarterly?
 
A. 8.25 percent
B. 8.49 percent
C. 8.38 percent
D. 8.51 percent
E. 8.56 percent
D. 8.51 percent
 
EAR = [1 + (.0825 /4)]⁴- 1 = .0851, or 8.51 percent
   
Capstone Investments is considering a project that will produce cash inflows of
$11,000 at the end of Year 1,
$24,000 in Year 2
$36,000 in Year 3.
What is the present value of these cash inflows at a discount rate of 12 percent?
 
$54,578.17
 
PV = ($11,000/1.12) + ($24,000/1.122^2) + ($36,000/1.123^3) = $54,578.17
   
ST Trucking just signed a $3.8 million contract.
The contract calls for a payment of $1.1 million today, $1.3 million one year from today, and $1.4 million two years from today.
What is this contract worth today at a discount rate of 8.7 percent?
 
$3,480,817.37
 
PV = $1.1m + ($1.3m/1.087) + ($1.4m/1.0872) = $3,480,817.37
   
Eric is considering an investment that will pay $8,200 a year for five years, starting one year from today.
What is the maximum amount he should pay for this investment if he desires a rate of return of 11.2 percent?
 
$30,154.50
 
PV of an Annuity = $8,200 × {1 - [1 / (1 + .112)⁵]} / .112 = $30,154.50
   
How much money does Suzie need to have in her retirement savings account today if she wishes to withdraw $42,000 a year for 25 years?
She expects to earn an average rate of return of 9.75 percent.
 
$388,683.83
 
PV of an Annuity = $42,000 × {1 - [1 / (1 + .0975)²⁵]} / .0975 = $388,683.83
   
Which one of the following statements concerning annuities is correct?
 
A. The present value of an annuity is equal to the cash flow amount divided by the discount rate.
B. An annuity due has payments that occur at the beginning of each time period.
C. The future value of an annuity decreases as the interest rate increases.
D. If unspecified, you should assume an annuity is an annuity due.
E. An annuity is an unending stream of equal payments occurring at equal intervals of time.
   
Suenette plans to save:
$600 at the end of Year 1
$800 at the end of Year 2
$1,000 at the end of Year 3.
If she earns 3.4 percent on her savings, how much money will she have saved at the end of Year 3?
 
A. $2,200.00
B. $2,238.47
C. $2,468.69
D. $2,309.16
E. $2,402.19
   
A credit card has an annual percentage rate of 12.9 percent and charges interest monthly.
The effective annual rate on this account:
 
A. will be less than 12.9 percent.
B. can either be less than or equal to 12.9 percent.
C. is 12.9 percent.
D. can either be greater than or equal to 12.9 percent.
E. will be greater than 12.9 percent.
   
You want to purchase a new condominium that costs $287,500.
Your plan is to pay 25 percent down in cash and finance the balance over 15 years at 3.75 percent.
What will be your monthly mortgage payment including principal and interest?
 
Amount financed = (1 - .25) ×$287,500 = $215,625
PV = $215,625 = C × (1 - {1 / [1 + (.0375 / 12)]¹⁸⁰}) / (.0375 / 12) C = $1,568.07
   
Today, you are purchasing a 20-year, 6 percent annuity at a cost of $48,350.
The annuity will pay annual payments starting one year from today. What is the amount of each payment?
 
PV = $48,350 = C × {1 - [1 / (1 + .06)²⁰]} / .06 C = $4,215.37
   
Industrial Tools owes you $38,600.
This amount is seriously delinquent so you have offered to accept weekly payments for one year at an interest rate of
3 percent to settle this debt in full. What is the amount of each payment?
 
$753.71
 
PV = $38,600 = C × (1 - {1 / [1 + (.03 / 52)]52}) / (.03 / 52)
C = $753.71
   
Karley's setting aside $32,000 each quarter, starting today, for the next three years for an expansion project.
How much money will the firm have at the end of the three years if it can earn an average of 5.45 percent on its savings?
 
FV = $32,000 ×{[1 + (.0545 / 4)]^^{12 - 1}} / (.0545 / 4)× [1 + (.0545 / 4)] = $419,766.30
   
Janice plans to save $80 a month, starting today, for 20 years. Kate plans to save $80 a month for 20 years,
starting one month from today. Both Janice and Kate expect to earn an average return of 5.5 percent on their savings.
At the end of the 20 years, Janice will have approximately _____ more than Kate.
 
$159.73
 
FVJ = $80 × {[1 + (.055 / 12)]^{240 - 1}} / (.055 / 12) × [1 + (.055 / 12)] = $35,009.92
FVK = $80 × {[1 + (.055 / 12)]^{240 - 1}} / (.055 / 12) = $34,850.19
Difference = $35,009.92 - 34,850.19 = $159.73
   
At the end of this month, Les will start saving $200 a month for retirement through his company's retirement plan.
His employer will contribute an additional $.50 for every $1.00 that he saves.
If he is employed by this firm for 30 more years and earns an average of 8.25 percent on his retirement savings,
how much will he have in his retirement account 30 years from now?
 
$470,465.70
 
Total monthly contribution = $200 + (.5 ×$200) = $300
FV = $300 ×{[1 + (.0825 / 12)]^{360 - 1}} / (.0825 / 12) = $470,465.70
   
Alexis plans to invest $2,500 a year for 30 years starting at the end of this year.
How much will this investment be worth at the end of the 30 years if she earns an average annual rate of return of 9.6 percent?
 
$381,324.92
 
FV = $2,500 × [(1 + .096)^{30 - 1}] / .096 = $381,324.92
   
Uptown Insurance offers an annuity due with semiannual payments for 25 years at 6 percent interest.
The annuity costs $200,000 today. What is the amount of each annuity payment?
 
$7,546.70
 
PV = $200,000 = C × (1 - {1 / [1 + (.06 / 2)]⁵⁰}) / (.06 / 2)× [1 + (.06 / 2)]
C = $7,546.70
   
Lacey will receive $135,000 a year for 5 years, starting today.
If the rate of return is 8.9 percent, what are these payments worth today?
 
$573,323.90
 
PV = $135,000 × ({1 - [1 / (1 + .089)⁵]} / .089)× (1 + .089)
r = $573,323.90
   
A preferred stock pays an annual dividend of $4.50.
What is one share of this stock worth to you today if you require a rate of return of 11 percent?
 
$40.91
 
P = $4.50/.11 = $40.91
   
You would like to establish a trust fund that would provide annual scholarships of $100,000 forever.
How much would you have to deposit today in one lump sum to achieve this goal if you can earn a guaranteed 4.5 percent rate of return?
 
$2,222,222
 
P = $100,000 /.045 = $2,222,222
   
Standards Life Insurance offers a perpetuity that pays annual payments of $12,000.
This contract sells for $250,000 today. What is the interest rate?
 
0.0480, or 4.80 percent
 
r = $12,000/$250,000 = 0.0480
   
A preferred stock offers a rate of return of 5.45 percent and sells for $78.20?
What is the annual dividend amount?
 
$4.26
 
C = .0545 × $78.20 = $4.26
   
Anne plans to save $40 a week, starting next week,for ten years and earn a rate of return of 4.6 percent, compounded weekly.
After the ten years, she will discontinue saving and invest her account at 6.5 percent, compounded annually.
How long from now will it be before she has accumulated a total of $50,000?
 
20.32 years
 
FV = $40 × ({[1 + (.046 / 52)]^{520 - 1}} / (.046 / 52)) = $26,395.74
FV = $50,000 = $26,395.74 × (1 + .065)t
t = 10.32 years
Total time = 10 + 10.32 = 20.32 years
   
What is the value today of $3,600 received at the end of each year for eight years if the first payment is paid at the end
of Year 4 and the discount rate is 12 percent?
 
$12,729.12
 
PV3 = $3,600 × ({1 - [1 / (1 + .12)⁸]} / .12) × (1 + .12) = $17,883.50
PV0 = $17,883.50 / (1 + .12)3 = $12,729.12
   
You will receive annual payments of $800 at the end of each year for 12 years.
The first payment will be received in Year 3. What is the present value of these payments if the discount rate is 7 percent?
 
$5,549.96
 
PV2 = $800× ({1 - [1 / (1 + .07)¹²]} / .07) × (1 + .07) = $6,354.15
PV0 = $6,354.15 / (1 + .07)2 = $5,549.96
   
What is the effective annual rate of 8.25 percent compounded quarterly?
 
0.0851, or 8.51 percent
 
EAR = [1 + (.0825 /4)]⁴ - 1 = .0851, or 8.51 percent
   
Round House Furniture offers credit to its customers at a rate of 1.15 percent per month.
What is the effective annual rate of this credit offer?
 
0.1471, or 14.71 percent
 
EAR = (1 + .0115)¹² - 1 = 0.1471
   
What is the effective annual rate of 14.9 percent compounded quarterly?
 
0.1575, or 15.75 percent
 
EAR = [1 + (.149/4)]⁴ - 1 = 0.1575
   
A loan that compounds interest monthly has an EAR of 14.40 percent. What is the APR?
 
0.1353, or 13.53 percent
 
EAR = .1440 = [1 + (APR/12)]^{12- 1} = 0.1353, or 13.53 percent
   
Dixie's Markets offers credit to its customers and charges interest of 1.2 percent per month.
What is the effective annual rate?
 
0.1539, or 15.39%
 
EAR = (1 + .012)12- 1 = 0.1539
   
Sporting Goods charges .85 percent interest per month. What rate of interest are its credit customers actually paying?
 
0.1069, or 10.69 percent
 
EAR = (1 + .0085)12- 1 = 0.1069
   
You have an outstanding loan with an EAR of 14.61 percent. What is the APR if interest is compounded monthly?
 
0.1371, or 13.71 percent
 
EAR = .1461 = [1 + (APR / 12)]12 - 1
APR = 0.1371
   
The Rent-to-Own Store has a six-year, interest-only loan at 7.6 percent interest.
The firm originally borrowed $115,000. How much will the firm pay in total interest over the life of the loan?
 
$52,440.00
 
Total interest = $115,000 ×.076 ×6 = $52,440.00
   
Assume you pay $24,000 today in exchange for an annuity with monthly payments, an APR of 6.75 percent, and a life of 15 years.
What is the payment amount?
 
$212.38
 
PV = $24,000 = C × [(1 - {1 / [1 + (.0675 / 12)]180}) / (.0675 / .12)]
C = $212.38
   
You want to buy a new sports coupe for $84,600and the finance office at the dealership has quoted you an APR of 7.1 percent,
compounded monthly, for 72 months.
How much interest will you pay over the life of the loan assuming you make all payments on a timely basis?
 
$19,542
 
PV = $84,600 = C × [(1 - {1 / [1 + (.071 / 12)]72}) / (.071 /.12)]
C = $1,446.41
Total interest = ($1,446.41 × 72) - $84,600 = $19,542
   
Which statement is true?
 
A. All else equal, an ordinary annuity is more valuable than an annuity due.
B. All else equal, a decrease in the number of payments increases the future value of an annuity due.
C. An annuity with payments at the beginning of each period is called an
ordinary annuity.
D. All else equal, an increase in the discount rate decreases the present value and increases the future value of an annuity.
E. All else equal, an increase in the number of annuity payments decreases the present value and increases the future value of an annuity.
   
Which one of the following statements is correct?
A. The APR is equal to the EAR for a loan that charges interest monthly.
B. The EAR is always greater than the APR.
C. The APR on a monthly loan is equal to (1 + monthly interest rate)12- 1.
D. The APR is the best measure of the actual rate you are paying on a loan.
E. The EAR, rather than the APR, should be used to compare both investment and loan options.
   
Kurt will receive $1,200 a month for five years from an insurance settlement.
The first payment was received today. If he invests the full amount of each payment at a guaranteed 6.15 percent rate,
how much will he have saved at the end of the five years?
 
$84,478.33
 
FV = $1,200 × ({[1 + (.0615 / 12)]^{60 - 1}} / (.0615 / 12))× [1 + (.0615)] = $84,478.33
   
You want to buy a new sports coupe for $84,600and the finance office at the dealership has quoted you an APR of 7.1 percent,
compounded monthly, for 72 months.
How much interest will you pay over the life of the loan assuming you make all payments on a timely basis?
 
$19,542
 
PV = $84,600 = C × [(1 - {1 / [1 + (.071 / 12)]72}) / (.071 /.12)]
C = $1,446.41
Total interest = ($1,446.41 × 72) - $84,600 = $19,542
   
Katie's Dinor spent $113,800 to refurbish its current facility.
The firm borrowed 65 percent of the refurbishment cost at 6.82 percent interest for six years.
What is the amount of each monthly payment?
 
0.1539, or 15.39%
 
EAR = (1 + .012)12- 1 = .1539
   
A local magazine is offering a $2,500 grand prize to one lucky winner.
The prize will be paid in four annual payments of $625 each, starting
one year after the drawing. How much would this prize be worth to you if
you can earn 9 percent on your money?
 
$2,024.82
 
PV = (625/0.09)*(1-1.09^-4) = $2024.82
   
A credit card has an annual percentage rate of 12.9 percent and charges interest monthly.
The effective annual rate on this account:
 
will be greater than 12.9 percent.
   
Lacey will receive $135,000 a year for 5 years, starting today. If the rate of return is 8.9 percent,
what are these payments worth today?
 
$573,323.90
 
PV = $135,000×({1 - [1 / (1 + .089)⁵]} / .089)× (1 + .089)
r = $573,323.90
   
Best's Fried Chicken just took out an interest-only loan of $50,000 for three years with an interest rate of 8.15 percent.
Payments are to be made at the end of each year. What is the amount of the payment that will be due at the end of Year 3?
 
$54,075.00
 
Payment Year 3 = $50,000 + ($50,000 x .0815) = $54,075.00
   
Janice plans to save $80 a month, starting today, for 20 years. Kate plans to save $80 a month for 20 years,
starting one month from today. Both Janice and Kate expect to earn an average return of 5.5 percent on their savings.
At the end of the 20 years, Janice will have approximately _____ more than Kate.
 
$159.73
 
FVJ = $80 ×{[1 + (.055 / 12)]^{240 - 1}} / (.055 / 12) × [1 + (.055 / 12)] = $35,009.92
FVK = $80 ×{[1 + (.055 / 12)]^{240 - 1}} / (.055 / 12) = $34,850.19
Difference = $35,009.92 -34,850.19 = $159.73
   
Assume you can save
$8,500 at the end of Year 2,
$9,300 at the end of Year 3,
$7,100 at the end of Year 6.
If today is Year 0, what is the future value of your savings 10 years from now if the rate of return is 7.8 percent annually?
 
$40,822.55
 
FV Year 10= [$8,500 (1 + .078)8] + [$9,300 (1 + .078)7] + [$7,100 (1 + .078)4] = $40,822.55
   
Travis is buying a car and will finance it with a loan that requires monthly payments of $265 for the next four years.
His car payments can be described by which one of the following terms?
 
Annuity
   
A preferred stock pays an annual dividend of $4.50.
What is one share of this stock worth to you today if you require a rate of return of 11 percent?
 
$40.91
 
P = $4.50 /.11 = $40.91
   
Which one of the following features distinguishes an ordinary annuity, from an annuity due?
 
Timing of the annuity payments
   
Travis borrowed $10,000 four years ago at an annual interest rate of 7 percent.
The loan term is six years. Since he borrowed the money, Travis has been making annual payments of $700 to the bank.
Which type of loan does he have?
 
Interest-only
   
Bill just financed a used car through his credit union. His loan requires payments of $275 a month for five years.
Assuming that all payments are paid on time, his last payment will pay off the loan in full.
What type of loan does Bill have?
 
Amortized
   
What condition must exist if a bond's coupon rate is to equal both the bond's current yield and its yield to maturity?
Assume the market rate of interest for this bond is positive.
 
The bond must be priced at par.
   
What is the principal amount of a bond that is repaid at the end of the loan term called?
 
Face value
   
A bond's annual interest divided by its face value is referred to as the:
 
Coupon rate
   
The concept of the time value of money is based on the principle that a dollar today is worth ______ a dollar promised at some time in the future.
 
more than
   
Future value refers to the amount of money an investment is worth today.
 
False
   
If you invest for a single period at an interest rate of r, your money will grow to Blank______ per dollar invested.
 
(1 + r)
   
If you invest at a rate of r for periods, under compounding, your investment will grow to (1 + r)2 per dollar invested.
 
Two
   
The process of accumulating interest in an investment over time to earn more interest is called ______.
 
compounding
   
Why is a dollar received today worth more than a dollar received in the future?
 
Today's dollar can be reinvested, yielding a greater amount in the future.
   
Future value is the Blank______ value of an investment at some time in the future.
 
cash
   
Future value is the value of an investment at some time in the future.
 
monetary
   
FV = ______× (1 + r)^t
 
PV
   
If you invest for two periods at an interest rate of r, then your money will grow to (1 + r) per dollar invested.
 
false
   
Time value of money tables are not as common as they once were because:
 
it is easier to use inexpensive financial calculators instead.
they are available for only a relatively small number of interest rates.
   
If you invest at a rate of r for two periods, under compounding, your investment will grow to (1 + r)2 per dollar invested.
 
True
   
When entering the interest rate in a financial calculator, you should key in the interest rate as a decimal.
 
False
   
The idea behind______ is that interest is earned on interest.
 
compounding
   
Calculating the present value of a future cash flow to determine its worth today is commonly called Blank______ valuation.
 
discounted cash flow (DCF)
   
The amount an investment is worth after one or more periods is called the ______ value.
 
future
   
Which formula below represents a present value factor?
 
1/(1 + r)t
   
Which of the following is the multi-period formula for compounding a present value into a future value?
 
FV = PV × (1 + r)t
   
Which of the following methods are used to calculate present value?
 
a time value of money table
an algebraic formula
a financial calculator
   
Which of the following are the primary as well as easy ways used to perform financial calculations today?
spreadsheet functions


financial calculator
   
Given the PV, FV, and life of the investment, you can determine the discount rate.
 
True
   
To calculate the future value of $100 invested for t years at r interest rate, you enter the present value in your calculator as a negative number. Why?
 
because the $100 is an outflow from you which should be negative
   
Given the PV, FV, and payment amount, you can determine the number of periods.
 
False
   
The current value of a future cash flow discounted at the appropriate rate is called the Blank______ value.
 
present
   
The formula for a present value factor is 1/(1+r)t1/1+rt.
 
True
   
In a present value equation, the rate (r) can be found using the PV, FV, and t.
 
discount
   
Using the PV, discount rate, and _______, you can determine the number of periods.
 
FV
   
The beginning value of an account or investment in a project is known as its _________ _______.
 
present value
   
Using a savings account as an example, the difference between the account's present value and its future value at the end of the period is due to __________ earned during the period.
 
interest
   
The equation FVN = PV(1 + I)N determines the future value of a sum at the end of n periods. The factor (1 + I)N is known as the ________ _______ __________ ________.
 
future value interest factor
   
The process of finding present values is often referred to as _____________ and is the reverse of the _____________ process.
 
discounting; compounding
   
The PVIFI,N for a 5-year, 5 percent investment is 0.7835. This value is the ____________ of the FVIF for 5 years at 5 percent.
 
reciprocal
   
For a given number of time periods, the PVIF will decline as the __________ ______ increases.
 
interest rate
   
A series of payments of a constant amount for a specified number of periods is a(n) _________. If the payments occur at the end of each period it is a(n) __________ annuity, while if the payments occur at the beginning of each period it is an annuity _____.
 
annuity; ordinary; due
   
The present value of an uneven stream of future payments is the _____ of the PVs of the individual payments.
 
sum
   
Since different types of investments use different compounding periods, it is important to distinguish between the
quoted, or _________, rate and the ___________ annual interest rate.
 
nominal; effective
   
When compounding occurs more than once a year, divide the _________ ______ by the number of times compounding
occurs and multiply the years by the number of _____________ _________ per year.
 
nominal rate; compounding periods
   
______ _______ are used to help visualize what is happening in time value of money problems.
 
Time lines
   
An annuity that goes on indefinitely is called a(n) ____________.
 
perpetuity
   
___________ loans are those which are paid off in equal installments over time.
 
Amortized
   
The breakdown of each payment as partly interest and partly principal is developed in a(n) ______ ______________ __________.
 
loan, amortization, schedule
   
If money has time value (that is, I > 0), the future value of some amount of money will always be more than the amount invested.
The present value of some amount to be received in the future is always less than the amount to be received.


True
   
You have determined the profitability of a planned project by finding the present value of all the cash flows from that project.
Which of the following would cause the project to look less appealing, that is, have a lower present value?
a. The discount rate decreases.
b. The cash flows are extended over a longer period of time.
c. The discount rate increases.
d. Statements b and c are both correct.
e. Statements a and b are both correct.
   
As the discount rate increases without limit, the present value of a future cash inflow
a. Gets larger without limit.
b. Stays unchanged.
c. Approaches zero.
d. Gets smaller without limit; that is, approaches minus infinity.
e. Goes to eIN
  An ordinary annuity is best defined by which one of the following?

a. increasing payments paid for a definitive period of time
b. increase payments paid forever
c. equal payments paid at regular intervals over a stated time period
d. equal payments paid at regular intervals of time on an ongoing basis
e. unequal payments that occur at set intervals for a limited time period
   
Which statement is correct related to growing annuities and perpetuities?

a. the cash flow used in the growing annuity formula is the initial cash flow at time zero
b. growth rates cannot be applied to perpetuities if you wish to compute the present value
c. the future value of an annuity will decrease if the growth rate is increased
d. an increase in the rate of growth will decrease the present value of an annuity
e. the present value of a growing perpetuity will decrease if the discount rate is increased Some of the cash flow generated by a firm goes back to the financial markets in the form of ______.

A: Dividends and debt payments
B: Products and services
C: Taxes and other payments to the government
D: Reinvested cash flows

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