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65) A compound annuity involves depositing or investing a single sum of money and allowing it
to grow for a certain number of years.
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
66) When repaying an amortized loan, the interest payments increase over time.
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
67) An amortized loan is a loan paid in unequal installments.
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
68) A loan amortization schedule provides a breakdown of loan payments into principal and
interest payments.
Topic: 6.1 Annuities
Keywords: present value
Principles: Principle 1: Money Has a Time Value
69) Holding all other variables constant, payment per period for an annuity due will be higher
than an ordinary annuity.
Topic: 6.1 Annuities
Keywords: annuity due
Principles: Principle 1: Money Has a Time Value
70) If you have an opportunity cost of 10%, how much must you invest each year to have $4,000
accumulated in 10 years?
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
21
71) 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?
14 years
Topic: 6.1 Annuities
Keywords: present value of annuity
6.418 = PVIFA[? %, 10 periods]
i = 9%
Annual interest rate = (.09)(2) = .18 = 18%
Topic: 6.1 Annuities
Keywords: present value of annuity
14.947 = FVIFA[1%, n periods]
n = 14 months
Topic: 6.1 Annuities
Keywords: future value of annuity
74) 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?
18,000 PV
18 I/yr or I
N = Approximately 75 months = 6.25 years
Topic: 6.1 Annuities
Keywords: present value of annuity
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.
2 $69,815.01 $709.99 $523.61 $186.38 $69,628.63
Topic: 6.1 Annuities
Keywords: present value of annuity
18.914 = PVIFA[2%, ? periods] n = 24 months
Topic: 6.1 Annuities
Keywords: present value of annuity
77) 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?
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
1) 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
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
2) 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) .055
B) .010
C) .110
D) .220
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
24
3) 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
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
4) You are going to pay $800 into an account at the beginning of each of 20 years. The account
will then be left to compound for an additional 20 years. At the end of the 41st year you will
begin receiving a perpetuity from the account. If the account pays 14%, how much will you
receive each year from the perpetuity (round to nearest $1,000)?
A) $140,000
B) $150,000
C) $160,000
D) $170,000
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
5) You are considering the purchase of XYZ Company's perpetual preferred stock which pays a
14%, what is the price of one share of this stock?
A) $7.02
B) $57.14
C) $36.43
D) Cannot be determined without maturity date
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
25
6) Michael Bilkman has an opportunity to buy a perpetuity that pays $24,350 annually. His
required rate of return on this investment is 14.25%. At what price would Michael be indifferent
to buying or not buying the investment? Round off to the nearest $1.
A) $83,470
B) $170,877
C) $95,621
D) $121,709
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
7) What is the present value of a $200 perpetuity when the discount rate is 10%?
A) $2,000
B) $20,000
C) $4,000
D) $40,000
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
8) Your rich great, great aunt just passed away at the age of 91. She liked you more than she let
on and left you in her will. You will receive 100 British bonds that pay interest forever. The
amount of annual interest payments that you will receive is $5,000. If you could invest your
money at 4.25%, how much are these bonds worth today?
A) $64,480
B) $197,250
C) $250,000
D) $117,647
E) $55,000
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
9) A bond paying interest of $120 per year forever is an example of a perpetuity.
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
26
10) The formula for calculating the present value of a perpetuity is P = A/(1 + i).
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
11) A perpetuity is an investment that continues forever but pays a different dollar amount each
year.
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
12) The present value of a $100 perpetuity discounted at 5% is $1200.
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
13) All else constant, an individual would be indifferent between receiving $2,000 today or
receiving a $200 perpetuity when the discount rate is 10% annually.
Topic: 6.2 Perpetuities
Keywords: perpetuity
Principles: Principle 1: Money Has a Time Value
14) If your opportunity cost is 12%, how much will you pay for a bond that pays $100 per year
forever?
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
27
15) What is the present value of the following perpetuities?
a. $600 discounted at 7%
b. $450 discounted at 12%
c. $1,000 discounted at 6%
d. $880 discounted at 9%
Topic: 6.2 Perpetuities
Keywords: present value of a perpetuity
Principles: Principle 1: Money Has a Time Value
1) What is the value on 1/1/05 of the following cash flows? Use a 10% discount rate, and round
your answer to the nearest $10.
1/1/11 $500
A) $490
B) $460
C) $970
D) $450
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
28
2) Consider the following cash flows:
1/1/10 $100
What is the value on 1/1/05 of the above cash flows? Use an 8% discount rate, and round your
answer to the nearest $10.
A) $600
B) $620
C) $630
D) $650
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
3) If you put $200 in a savings account at the beginning of each year for 10 years and then allow
the account to compound for an additional 10 years, how much will be in the account at the end
of the 20th year? Assume that the account earns 10%, and round to the nearest $10.
A) $8,300
B) $9,100
C) $8,900
D) $9,700
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
4) An investment is expected to yield $300 in three years, $500 in five years, and $300 in seven
years. What is the present value of this investment if our opportunity rate is 5%?
A) $735
B) $865
C) $885
D) $900
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
29
